SCICADE2026: SCIENTIFIC COMPUTING AND DIFFERENTIAL EQUATIONS

This page contains an index consisting of author-provided keywords.

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$\varphi$-order conditions	Stiffness resilient exponential integrators
$H^{\mathrm{dev}}(\mathrm{Curl})$-conforming elements	Intrinsic $H^{\mathrm{dev}}(\mathrm{Curl})$-conforming elements for planar relaxed micromorphic models
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(LCHS)	Schrödingerization for quantum linear systems problems with near-optimal dependence on matrix queries
1
1-Lipschitz integrators	Stability of Numerical Integrators on Riemannian Manifolds
2
2D fluid dynamics	Two-dimensional fluids via matrix hydrodynamics
3
3d-1d	A 3D-1D model of the electrostatic problem on the electrical treeing
A
A posteriori error estimation	Adaptive Minimal Residual Methods for Parabolic Problems on Locally Refined Space-Time Meshes
a priori analysis	Finite element discretization of nonlinear models of ultrasound heating
a priori and a posteriori error estimate	A Priori and a Posteriori Error Estimate for Pressure Robust Schemes for Incompressible Flow
A priori error estimates	On the numerical analysis of mean-field models for electronic structure calculations in perfect crystals
A-stability	Error and Stability Analysis of a Randomized SDIRK Method
accelerated spreading	Nonlocal Fisher-KPP Equation with Free Boundaries: Numerical Strategies for Accelerated Spreading and Sensitivity Analysis
acoustic scattering	A Cartesian Grid-based Boundary Integral Method for Acoustic Scattering
active Brownian particles	Transitions in proliferating active matter — particle-based simulations and effective models
active matter	Stochastic processes with division, death and diffusion Reentrance in a Hamiltonian flocking model Computational geometry of active matter: Space to insert hard spheres Modelling disordered non-reciprocal active solids
active polymers	Nonequilibrium polymer models for chromatin replication
adaptive first-order methods	mdBFGS: a Diagonal BFGS Method with Momentum for Stochastic Optimisation
adaptive integration	Accelerating Real-Time Boltzmann Transport Simulations with Adaptive Multirate Methods
Adaptive Langevin thermostat	Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling
Adaptive meshing	Graph Neural Networks for r- and hr-Adaptive Meshing in Finite Element Methods
Adaptive Multilevel Splitting	Importance sampling for Adaptive Multilevel Splitting
Adaptive rank	Domain decomposition dynamical low-rank for multi-dimensional radiative transfer equations
adaptive sampling	Moving sample method for solving time-dependent partial differential equations
adaptive size sampler	Adaptive Stepsizing for Stochastic Gradient Langevin Dynamics in Bayesian Neural Networks
Adaptive SOE	A Fast BDF2 Convolution Quadrature for Reaction-Diffusion Equations with Time-Dependent Memory
adaptive time discretization	Goal-Oriented Time Adaptivity For Linear pH-DAEs Of Index-1
Adaptive time-step	A IMEX-based spectral scheme with adaptive time-stepping for the Vlasov-Poisson system in the quasi-neutral limit
adaptivity	A posteriori estimates and adaptive boundary elements for the wave equation An Adaptive Gaussian-Based Time Integrator for Fokker–Planck Equations
Additive Manufacturing	Shape and topology optimization for additive manufacturing processes
ADI technique	Computationally Efficient Two-Grid ADI Scheme for Two-Dimensional Nonlinear Time-Fractional Reaction–Diffusion Equations
Adjoint state method	One Step Forward, One Step Back: A Memory-Efficient Dynamical Low-Rank Scheme for the Adjoint State Method
adjoint systems	Geometric Adjoint Sensitivity Analysis and Hamiltonian Variational Integrators
Adjoint-based optimization	Adjoint Monte Carlo Simulation of Kinetic Equations with Reversible Random Number Generators
advection-diffusion problems	Finite element exterior calculus for spectra and pseudo-spectra of advection-diffusion of differential forms
Advection-diffusion-reaction PDEs	Problem-oriented W-methods for advection-diffusion-reaction PDEs arising in vegetation dynamics
adversarial attacks	Low Rank Affine Adversarial Attacks on Image Classifiers
adversarial robustness	Reversible numerical integrators for memory efficient deep learning
agent-based models	Agent-based models in Opinion Dynamics: model reduction and mean-field limits
Aggregation-diffusion equation	Energy-Dissipative and Conservative Discrete Gradient Particle Methods for Aggregation-Diffusion Equations and the Landau Equation
AI	Learning Physics Directly From Corrupted Data.
AI4Science	FourCastNet 3: Geometric Neural Operators for Probabilistic Machine Learning Weather Forecast at Scale
Algebraic decay	High-Precision Hilbert Transform from Discrete Uniform Samples: Extracting Non-Integer Algebraic Decay Orders via the Matrix Pencil Method
Algebraic structures	Structure-preserving low-regularity integrators for dispersive nonlinear equations
Allen--Cahn equation	An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
Allen-Cahn equation	From Fabrication to Efficiency of Organic Photovoltaics: Modelling morphology and device performance
Alternating direction method of multipliers	Overcoming Logarithmic Singularities in the Cahn-Hilliard Equation with Flory-Huggins Potential: An Unconditionally Convergent ADMM Approach
Alternating Neural Integrators	Reliable Forecasting via Physics-Guided Stochastic Augmentation
alternating projections	Convergence and error estimates for P_1 finite element method for the Monge-Ampère equation
American option pricing	A Deep Neural Network for Pricing American Options under Jump-Diffusion in High Dimension: A Backward Stochastic Differential Equation Approach
analytical approximation	Analytical Approximation of Nonlinear Friedrichs Systems by Modulated Fourier Expansions
Anderson acceleration	Low-Rank Anderson Acceleration for Nonlinear Matrix and Tensor Equations
anisotropic surface energy	High-order parametric local discontinuous Galerkin methods for anisotropic 1 curve-shortening flows
anisotropy	Error estimates for a finite element method for anisotropic mean curvature flow Energy stable auxiliary variable method for Cahn--Hilliard equations
applications	Recent progress, gaps and opportunities in extended-MHD modelling for fusion energy applications
Applications to climate and environmental science	An Entropy-Stable Discontinuous Spectral-Element Method for the Spherical Shallow Water Equation
approximate domain boundaries	Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
approximation	Learning Green's functions from data Global space-time low-complexity numerical methods for the time-dependent Schrödinger equation
approximation by sum of exponentials	Solving time fractional ODEs and PDEs.
approximation of invariant measures	Ergodicity and invariant measure approximation of the stochastic Cahn–Hilliard equation via an explicit fully discrete scheme
Approximation theory	Neural Networks as a Discretization of Dynamical Systems Constructive Conditional Normalizing Flows Functional Data Analysis Using Neural Networks
arbitrary Lagrangian-Eulerian	An arbitrary Lagrangian--Eulerian sliding interface method for fluid-structure interaction with a rotating rigid structure
Arbitrary Lagrangian–Eulerian (ALE) methods	Arbitrary Lagrangian–Eulerian Schemes for Moving Interface Problems
Arbitrary-order discretization	A unified arbitrary-order Bernstein-Bézier discretization of H(div), H^1 and L^2 for 2D multi-physics problems
Aromatic bicomplex	Numerical preservation of measures of ODEs and SDEs with aromatic structures
Aromatic trees	Numerical preservation of measures of ODEs and SDEs with aromatic structures
Artificial intelligence	AI weather forecasting: Past, present and future Necessary mechanisms for super AI and stopping hallucinations: The consistent reasoning paradox and the indeterminacy function
artificial neural networks	Deterministic and probabilistic rounding error analysis of artificial neural networks in floating-point arithmetic
Asymmetric interacting particle systems	Data-driven Discovery of Asymmetric Interacting Particle Systems
asymptotic convergence	Energy-stable inertial level-set flow for topology optimization
asymptotic expansion	Entropic metastability in the narrow escape problem
asymptotic-preserving	Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations
Asynchronous discontinuous Galerkin	Scalability of high-dimensional Vlasov-Poisson simulations with communication-avoiding asynchronous discontinuous Galerkin
Atmosphere-ocean	Treating different timescales in variational data assimilation for coupled systems
Atomic Energy	Accelerated Machine Learning Atomic Energy and Force Predictions via Fast Kernel Summation
Atrial Fibrillation	Multimodal prediction of catheter ablation outcomes in patients with persistent atrial fibrillation
Audio Signal Processing	Low-rank factorization for music audio signals analysis
Autocovariance error	Markovian Approximation for Nonlinear Overdamped Langevin Systems
autodiff	Autodiff of Neural networks and application to DeepRitz and FEM
auxiliary variables	A stabilised auxiliary variable approach and its higher order schemes for gradient flows
average dwell-time	Impulsive Switched Systems with Mixed Dynamics: Lyapunov-Based Analysis of Finite-Time Input-to-State Stability
Avoiding order reduction in time	Exponential Rosenbrock Methods without order reduction when integrating nonlinear initial boundary value problems
Axisymmetric Open Surfaces	Magnetostatic scattering from axisymmetric open surfaces
B
B-series	Backward Error Analysis of Isospectral Integrators via Lie–Poisson Reduction of Butcher Series
backward difference method	Error estimates for backward difference full discretization of Willmore flow for surfaces
backward error	Deterministic and probabilistic rounding error analysis of artificial neural networks in floating-point arithmetic
Backward error analysis	Backward Error Analysis of Isospectral Integrators via Lie–Poisson Reduction of Butcher Series
Backward stochastic differential equation	A Deep Neural Network for Pricing American Options under Jump-Diffusion in High Dimension: A Backward Stochastic Differential Equation Approach
Backward stochastic differential equations	Positivity-Preserving Deep Density Filters for High-Dimensional SDEs
Baker-Campbell-Hausdorff formula	Error bounds for the truncated Baker-Campbell-Hausdorff formula
Barrier method	Efficient solvers for p-Laplace and related problems
Basis Update & Galerkin integrator	Efficient State/Parameter Estimation via Dynamical Low-Rank Kalman Filters
Bayesian filtering	Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems A Pontryagin Maximum Principle on the Belief Space for Continuous-Time Stochastic Optimal Control with Discrete Observations
Bayesian inference	Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations Sequential Monte Carlo for Bayesian Inference Using Randomized Likelihoods
Bayesian networks	Graph-informed GANs: Variational learning with Bayesian network structure
Bayesian Nonparametrics	Statistical Frameworks for Learning Nonlinear Mappings in Infinite Dimensions
Bayesian optimization	Bayesian Optimization on Networks
Bayesian sampling	Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling
Bayesian statistics	Positivity-Preserving Deep Density Filters for High-Dimensional SDEs
BDF2-Convolution quadrature	A Fast BDF2 Convolution Quadrature for Reaction-Diffusion Equations with Time-Dependent Memory
beam heating	Global optimization in very rugged landscapes for a kinetic beam heating problem
belief dynamics	A Pontryagin Maximum Principle on the Belief Space for Continuous-Time Stochastic Optimal Control with Discrete Observations
Bernstein-Bézier basis	A unified arbitrary-order Bernstein-Bézier discretization of H(div), H^1 and L^2 for 2D multi-physics problems
Bifurcation	Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos
bifurcation phenomena	A numerical investigation of the Hopf bifurcation occurring in quasi-geostrophic channel flow
bifurcations	Patterns and bifurcations in space-fractional reaction-diffusion models
Bilevel optimization	A functional approach to differential programming in machine learning Inexact Algorithms for Bilevel Learning
billiards	Numerical integrators for Langevin dynamics with boundary conditions
blow-up	Numerical study of biharmonic and polyharmonic nonlinear Schrödinger equations
blow-up finite elements	Two approaches to tensor fields on surfaces
BOLD signal	Learning Image Derived PDE-Phenotypes from fMRI Data
Boltzmann equation	Telescopic Projective Integration and Stochastic Galerkin for the Boltzmann Equation with Uncertainty
Boltzmann Generators	Machine Learning for Coarse-Grained Molecular Sampling
Boris algorithm	Variational Gaussian approximation for the magnetic Schrödinger equation
Boundary Conditions	Numerical study of dynamical regimes in the Landau–Lifshitz–Gilbert equation A qualitative study of the reflected Kinetic Langevin process
boundary control	Boundary Consensus of Reaction-Diffusion Multi-Agent Systems under Restricted Observation
boundary integral equations	Magnetostatic scattering from axisymmetric open surfaces A posteriori estimates and adaptive boundary elements for the wave equation Time dependent acoustic scattering in full space from penetrable objects with nonlinearities
boundary integral method	A Cartesian Grid-based Boundary Integral Method for Acoustic Scattering
Boundary integral methods	Geometric generalization of neural operators from kernel integral perspective
Boundary layer flow	Evaluating Global Scale Numerics on Small Scale Flows
Boussinesq equations	Iterative Solvers for Implicit Discretisations of the Boussinesq System via Patch-Wise Preconditioning
Brinkman penalization method	Geometric Property of the Brinkman Penalization Method for Hamiltonian PDEs and Its Applications
Bulk-surface PDE Modeling	A Thermodynamically Consistent Bulk-Surface PDE Model for Morphogen-Driven Receptor Dynamics and Lipid Raft Patterning
Buoyancy-Driven Flows	Numerical Analysis of the Evolve-Filter-Relax Reduced Order Model for Buoyancy-Driven Flows
Butcher series	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds Numerical preservation of measures of ODEs and SDEs with aromatic structures
C
Cahn--Hilliard equation	Energy stable auxiliary variable method for Cahn--Hilliard equations
Cahn-Hilliard	Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamics
Cahn-Hilliard equation	Overcoming Logarithmic Singularities in the Cahn-Hilliard Equation with Flory-Huggins Potential: An Unconditionally Convergent ADMM Approach Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models
Cahn-Hilliard equations	From Fabrication to Efficiency of Organic Photovoltaics: Modelling morphology and device performance
Cahn-Hilliard-Navier-Stokes	A thermodynamically consistent domain embedding model for Cahn-Hilliard-Navier-Stokes equations with generalized Navier-slip boundary conditions
Calculus of variations	From fractional variational principles to classical optimization
Canonical molecular dynamics	Mean-Field Molecular Dynamics Approximation of Quantum Statistical Observables with Machine Learning
canonical polyadic decomposition	Swamp crossing methods for the canonical polyadic decomposition
capillary folding	Contact Line Dynamics on Elastic Sheets
Caputo derivative	Recent Advances in Spectrally Accurate Collocation Methods for Fractional Modelling
Caputo–Fabrizio derivative	Nonlocal Delay Problems Driven by the Caputo–Fabrizio Operator
Carleman linearization	Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
Cartesian grid method	A Cartesian Grid-based Boundary Integral Method for Acoustic Scattering
cell growth and division	Transitions in proliferating active matter — particle-based simulations and effective models
Cell image segmentation，	A Multiscale Hierarchical Segmentation Framework for Cell Fluorescence Microscopy
Chan–Vese model	A Multiscale Hierarchical Segmentation Framework for Cell Fluorescence Microscopy
Chaos	Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos
Chebyshev methods	Second order explicit stabilized multirate method for stiff differential equations with error control Explicit stabilized implementation of singly diagonally implicit Runge-Kutta methods
Chemical accuracy	Towards spectral element solutions of full-potential Kohn-Sham equation
Cholesky factorization	Computing Cholesky-factors of finite-horizon Gramians
chromatin	Nonequilibrium polymer models for chromatin replication
Clifford+T rotation synthesis	Significantly more efficient Clifford+T synthesis for small-angle rotations and application to Trotterization
clustering dynamics	Coarse-Grained Modeling of Clustering Dynamics in Interacting Particle Systems
co-evolution	Agent-based models in Opinion Dynamics: model reduction and mean-field limits
Coarse Graining	Consistent Projection of Langevin Dynamics: Preserving Thermodynamics and Kinetics in Coarse-Grained Models Machine-learned coarse-graining for everything and everyone
Coarse-Graining	Coarse-Grained Molecular Sampling with Machine Learning Coarse-Grained Modeling of Clustering Dynamics in Interacting Particle Systems Preserving Transition Rates in Coarse-grained Models with Koopman Methods Machine Learning for Coarse-Grained Molecular Sampling
coarsening rate	Energy stable auxiliary variable method for Cahn--Hilliard equations
code Radau5	Solving time fractional ODEs and PDEs.
Coffee-ring phenomena	Variational Modelling and Numerical Simulations for Evaporating Thin Droplets and Coffee-Ring Effect
Collective Variables	AI and Molecular Dynamics: a theoretical perspective on why generative models can boost sampling
Committor	Importance sampling for Adaptive Multilevel Splitting
Communication-avoiding algorithms	Scalability of high-dimensional Vlasov-Poisson simulations with communication-avoiding asynchronous discontinuous Galerkin
community detection	Spectral clustering of temporal networks via spatio-temporal random walks
Commutator-scaling property	Error bounds for the truncated Baker-Campbell-Hausdorff formula
Compatibility conditions	Arbitrary high order splitting methods for linear Schrödinger equations with non-trivial compatibility conditions
Compatible finite elements	Fully implicit timestepping methods for the rotating shallow water equations
complex quantum states	Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
complexity	Global space-time low-complexity numerical methods for the time-dependent Schrödinger equation
Complexity of PDEs	A Variational Framework for the Algorithmic Complexity of PDEs
Compression	FeDLRT: Federated Dynamical Low-Rank Training
Compressive sensing	Scientific Data Reduction Methods
Computational complexity	On the optimal overlap in Optimized Schwarz Methods under computational cost constraint
Computational Electromagnetics	Structure-preserving Magnetic Relaxation in Stellarator Geometries
Computational finance	A Deep Neural Network for Pricing American Options under Jump-Diffusion in High Dimension: A Backward Stochastic Differential Equation Approach
Computational fluid dynamics	An end-to-end quantum algorithm for nonlinear fluid dynamics with bounded quantum advantage A numerical investigation of the Hopf bifurcation occurring in quasi-geostrophic channel flow Generalization Bounds for PINNs Solving the Navier-Stokes Equations
computational plasma physics	Geometric Numerical Discretization of Fully Kinetic and Hybrid Drift-Kinetic Electromagnetic Quasineutral Models
Computational uncertainty quantification	A filtering approach to quantifying discretisation errors in solving evolution equations Approximating distributions through greedy mixtures: an algorithmic framework.
Computer simulation	Accurate and robust analysis of molecular kinetics with random features
condensed matter physics	Graph zeta methods for efficient simulations of long-range interacting quantum lattices
Conditional Normalizing Flows	Reliable Forecasting via Physics-Guided Stochastic Augmentation
Conditional propagation of chaos	Convergence speed in distribution of finite particle systems to McKean-Vlasov-type equations using generators of measure-valued diffusions
Conditional Sampling	Constructive Conditional Normalizing Flows
Conformal symplectic structure	Conformal Symplectic Neural Networks for Learning Multiple Energy-Dissipative Systems
Connection one-form	Approximation of connection one-forms with finite elements
conservation	An energy and entrophy-conserving enriched Galerkin method for incompressible Navier-Stokes equations
conservation laws	Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables
Conservative discretisations	Stabilising conservative numerical methods with preconditioners
conservative numerical schemes	Two-dimensional fluids via matrix hydrodynamics
Consistency and stability analysis	Problem-oriented W-methods for advection-diffusion-reaction PDEs arising in vegetation dynamics
Consistent reasoning paradox	Necessary mechanisms for super AI and stopping hallucinations: The consistent reasoning paradox and the indeterminacy function
consistent transformations	Intrinsic $H^{\mathrm{dev}}(\mathrm{Curl})$-conforming elements for planar relaxed micromorphic models
Constrained sampling	Numerical integrators for Langevin dynamics with boundary conditions
constraints	Goal-Oriented Low-Rank Tensor Decompositions for Numerical Simulation Data Realisation of constraints in underdamped Langevin dynamics Numerical methods for constraint Langevin dynamics with complex heat bath models
contact Hamiltonian systems	Integrable Splitting for Polynomial Dynamical Systems
Contact mechanics	Modeling and simulation of fluid-structure-contact interaction
contact Noether's theorem	Discrete Contact Mechanics from the Herglotz Variational Principle
contact system	Discrete Contact Mechanics from the Herglotz Variational Principle
continuous formulations of numerical schemes	Low-regularity integrators for nonlinear dispersive equations via continuous formulations of numerical schemes
Continuous interior penalty	Unified numerical analysis for thermoelastic diffusion and thermo-poroelasticity of thin plates
continuous Petrov--Galerkin	Arbitrary-order structure-preserving discretizations for geometric curvature flows
Continuum	Atomistically-Informed Modelling of Dislocation Loops in Tungsten
contraction	Long-time behaviour of kinetic Langevin sampler
Control	One Step Forward, One Step Back: A Memory-Efficient Dynamical Low-Rank Scheme for the Adjoint State Method
Control Theory	Neural Networks as a Discretization of Dynamical Systems
controllability	Interpolation, approximation, and controllability of deep neural networks
Convection diffusion equations	Machine Learning-Enhanced Multigrid for Convection-Dominated Flows
Convection-Diffusion systems	Higher Order Unfitted Space-Time Finite Element Methods
convection–diffusion model	Leak localisation with a measure source convection–diffusion model
Convergence	Convergence of flexible GMRES with and without randomized sketching Energy-stable numerical methods for two-phase viscoelastic flows Wasserstein Bounds for generative diffusion models with Gaussian tail targets
convergence analysis	Computing Cholesky-factors of finite-horizon Gramians
Convergence guarantees	Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
convergence in probability	Numerical approximations of stochastic time-fractional Burgers equations with fractional Gaussian noise
Convergence of subdivision schemes	Multivariate vector subdivition schemes with a general matrix-valued filter
Convergence rate	Computer-Assisted Search for Differential Equations Corresponding to Optimization Methods and Their Convergence Rates
Convergence to equilibrium	Stratonovich perturbation to improve the convergence to equilibrium
Convex optimization	Efficient solvers for p-Laplace and related problems Computer-Assisted Search for Differential Equations Corresponding to Optimization Methods and Their Convergence Rates
convolution quadrature	Time-domain integral equations for the wave equation on moving domains Time dependent acoustic scattering in full space from penetrable objects with nonlinearities Numerical approximations of stochastic time-fractional Burgers equations with fractional Gaussian noise
Convolution quadrature methods	Subdiffusion Models with Evolving Memory Governed by Scarpi-Type Kernels
Coordinate Descent	Fast Algorithms for Full Configuration Interaction
corner singularities	Efficient and accurate spectral methods for PDEs in complex domains
correlation function	Vibrationally resolved electronic spectra from Hagedorn wavepacket dynamics
Correlation observable	Mean-Field Molecular Dynamics Approximation of Quantum Statistical Observables with Machine Learning
Cosserat beam networks	Numerical Analysis of Nonlinear Beam Networks
Cosserat Continuum	Analysis of a Phase Field Topology Optimization Problem with Cosserat Continuum and Thermal Dissipation
Cosserat micropolar model	A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity
Coupled models	Treating different timescales in variational data assimilation for coupled systems
coupled oscillators	Quantum Elastic Network Models and their Application to Graphene
Coupled Oscillatory Neural Networks	Stuart-Landau Oscillatory Graph Neural Network
couplings	Long-time behaviour of kinetic Langevin sampler
covariate shift	Unbounded Density Ratio Estimation and Its Application to Covariate Shift Adaptation
Cox-Voinov relation	Contact Line Dynamics on Elastic Sheets
cross approximation	A tensor train numerical approach for Boltzmann equation
Cross-diffusion Systems	A Thermodynamically Consistent Bulk-Surface PDE Model for Morphogen-Driven Receptor Dynamics and Lipid Raft Patterning
CUR	Cross Algorithms for Dynamical Matrix and Tensor Low-Rank Approximation in Fluid Mechanics
Curse of dimensionality	A Fast Algorithm for the Fractional Fokker–Planck Equation in Arbitrary Dimensions
Curvature	Approximation of connection one-forms with finite elements
Curvilinear mesh	A Curvilinear Lagrangian discontinuous Galerkin method for resistive magneto-hydrodynamics
Cut finite element method	Strong Stability of Cut Finite Element Methods for Parabolic Problems on Evolving Surfaces
Cut finite element methods	Conservative space–time CutFEM for variable surface-tension two-phase flow
Cut-FEM	Modeling and simulation of fluid-structure-contact interaction
cutFEM	Higher-order unfitted FEM for Stokes with strongly divergence-free velocity up to the boundary
D
DAEs	New Features and Applications in the SUNDIALS Library Goal-Oriented Time Adaptivity For Linear pH-DAEs Of Index-1
Darcy-Forchheimer equation	Machine Learning Assisted Two-Level Mixed Finite Element Method for the Darcy--Forchheimer Model
Data Assimilation	A Diffusion Model-Based Approach for Uncertainty Reduction in Learning Data-Driven Dynamical Systems Dynamical Low-Rank Filters for Data Assimilation Generative AI for Uncertainty Quantification and Data Assimilation Variational data assimilation in the latent space of an implicit-rank-minimising autoencoder
data requirements	Reducing Requirements on Data by Incorporating Structure
Data-driven learning	Heterogeneous Dictionaries Approximate Koopman Invariance: Why Deep Koopman Operators Work From Koopman to polynomial embeddings for data-driven learning of nonlinear dynamics
Data-driven method	Weak-form PDE Identification with Optimal Test Functions Learned from Data
Data-driven Modeling	Consistent Projection of Langevin Dynamics: Preserving Thermodynamics and Kinetics in Coarse-Grained Models Data-driven Discovery of Asymmetric Interacting Particle Systems
data-driven PDE discovery	Laplacian Eigenfunction-Based Neural Operator for Learning Nonlinear Reaction–Diffusion Dynamics
data-driven system identification	Discovering Piecewise-Smooth Dynamics from Trajectory Data
de Rham complex	A polytopal discrete de Rham scheme for Einstein's equations
Dean-Kawasaki equation	A discontinuous Galerkin method for the Dean-Kawasaki equation
decorated tree series	From explicit formulas to Wave Kinetic theory for the Benjamin–Ono equation
decoupling	Decoupling Time Stepping Schemes for Poroelasticity
Deep Generative Models	Coarse-Grained Molecular Sampling with Machine Learning Machine Learning for Coarse-Grained Molecular Sampling
Deep learning	A functional approach to differential programming in machine learning Heterogeneous Dictionaries Approximate Koopman Invariance: Why Deep Koopman Operators Work Geometric PDE-based Neural Networks for Image Processing Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model Structure preservation and Deep Learning for Learning Mechanical Systems from Data Hardware aware dynamical low-rank training of large language models Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States Positivity-Preserving Deep Density Filters for High-Dimensional SDEs A Deep Neural Network for Pricing American Options under Jump-Diffusion in High Dimension: A Backward Stochastic Differential Equation Approach Multimodal prediction of catheter ablation outcomes in patients with persistent atrial fibrillation A Nonlinear Tensor Network Architecture for Compressed End-to-End Learning
deep learning for PDEs	Weak Generative Sampler
deep neural networks	Interpolation, approximation, and controllability of deep neural networks
Deep-learning	Low-rank training of tensor-structured neural networks
DEIM	Cross Algorithms for Dynamical Matrix and Tensor Low-Rank Approximation in Fluid Mechanics
delay	Nonlocal Delay Problems Driven by the Caputo–Fabrizio Operator
Delay-Differential Equation	Error Analysis of Stabilized FEM for Singularly Perturbed Parabolic Delay-Differential Equations with Turning Point
Delayed multi-agent systems	Event-triggered $\mu$-consensus control for nonlinear MASs with unknown-bound delays under stochastic delayed impulses
density estimation	Permutation-structured function estimation via tensor-train sketching
density ratio	Unbounded Density Ratio Estimation and Its Application to Covariate Shift Adaptation
Derivative nonlinear Schrödinger equation	A low regularity exponential integrator for the DNLS equation
desingularisation	Geometric analysis of an epidemiological model for Olive Quick Decline Syndrome (OQDS)
DFT	Geometric methods for electronic dynamics and excited-state calculations
dictionary learning	Learning dynamical systems from data: Gradient-based dictionary optimization
dictionary-based learning	Heterogeneous Dictionaries Approximate Koopman Invariance: Why Deep Koopman Operators Work
Differentiable Programming	Firedrake: a differentiable programming framework for finite element simulation Structure-preserving Magnetic Relaxation in Stellarator Geometries
differential algebraic equations	Multirate infinitesimal solutions of DAEs arising in power system simulations
Differential equations	Intercardinal Splitting Approximations for Kawarada Equations with Cross-Derivative Terms Nearly optimal quantum simulation of slow time-dependent Hamiltonians Quantum algorithms and lower bounds for differential equations Quantum Elastic Network Models and their Application to Graphene Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
Differential equations with constraints	The unconventional Hug integrator
differential Lyapunov equation	Computing Cholesky-factors of finite-horizon Gramians
Differential Riccati equations	Convergence analysis for a full discretization of operator-valued differential Riccati equations
Differential-algebraic equations	Physics-consistent learning of circuit solutions using a topological decoupling of MNA Solving time fractional ODEs and PDEs.
diffuse domain	A thermodynamically consistent domain embedding model for Cahn-Hilliard-Navier-Stokes equations with generalized Navier-slip boundary conditions
Diffusion model	A Diffusion Model-Based Approach for Uncertainty Reduction in Learning Data-Driven Dynamical Systems Generative AI for Uncertainty Quantification and Data Assimilation Wasserstein Bounds for generative diffusion models with Gaussian tail targets
Diffusion models	Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
diffusion processes	Learning dynamical systems from data: Gradient-based dictionary optimization
diffusion-advection-reaction problems	Explicit stabilized implementation of singly diagonally implicit Runge-Kutta methods
Dimensionality reduction	Learning Image Derived PDE-Phenotypes from fMRI Data
Directional splitting	Exploring directional split exponential integrators: from theory to efficient implementation
Dirichlet-Neumann Waveform relaxation	Continuous and Time-discrete Error Bounds in the two norm for Waveform Relaxation for Heterogeneous Heat Equations
Discontinuous Galerkin	A Curvilinear Lagrangian discontinuous Galerkin method for resistive magneto-hydrodynamics A discontinuous Galerkin method for the Dean-Kawasaki equation
Discontinuous Galerkin method	A Discontinuous Galerkin solver as an alternative dynamical core for the ICON model Discontinuous Galerkin Methods for nonlinear wave equations via elliptic regularisation.
discontinuous Galerkin methods	Structure-Preserving Methods for the Compressible Euler Equations
Discontinuous inputs	Deep Predictor-Corrector Networks for Robust Parameter Estimation in Non-autonomous System with Discontinuous Inputs
discovery of dynamics	Approximation and Error Bounds for KANs: Applications to Dynamical System Discovery via Linear Multistep Methods
discrete differential geometry	Locking-free shells with structure-preserving mixed finite elements
Discrete Empirical Interpolation Method	Efficient State/Parameter Estimation via Dynamical Low-Rank Kalman Filters
discrete gradient	Energy-Dissipative and Conservative Discrete Gradient Particle Methods for Aggregation-Diffusion Equations and the Landau Equation
discrete Strichartz estimates	Error analysis of splitting methods for 3D semilinear wave equations with finite-energy solutions
discrete transport identities	Strong Stability of Cut Finite Element Methods for Parabolic Problems on Evolving Surfaces
Discretisation error	A filtering approach to quantifying discretisation errors in solving evolution equations
discretization	On the variational formulation and discretization of optimal control problems for Lagrangian dynamics
discretization error analysis	Error analysis for a finite element discretization of a radially symmetric harmonic map heat flow problem
Discretizations of ODEs	Trim turnpike property in discretized optimal control problems
Dislocations	Atomistically-Informed Modelling of Dislocation Loops in Tungsten
dispersion relation	Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations Energy stable auxiliary variable method for Cahn--Hilliard equations
dispersive equation	Exponential integrator for dispersive equations with concentrated potential
dispersive nonlinear partial differential equations	Structure-preserving low-regularity integrators for dispersive nonlinear equations From explicit formulas to Wave Kinetic theory for the Benjamin–Ono equation
dispersive PDEs	Approximating the Matrix Exponential for Large Time Steps High-Precision Hilbert Transform from Discrete Uniform Samples: Extracting Non-Integer Algebraic Decay Orders via the Matrix Pencil Method
Dispersive shallow water	Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
dissipation inequalities	Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables
dissipation law	Discrete Contact Mechanics from the Herglotz Variational Principle
Dissipative quantum dynamics	Dynamics of two-dimensional dissipative quantum spin systems using tree tensor networks
Distributed optimization	FeDLRT: Federated Dynamical Low-Rank Training
divergence free element	Higher-order unfitted FEM for Stokes with strongly divergence-free velocity up to the boundary
divergence-free vector fields	Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
divergences	Lipschitz-regularized gradient flows and generative particle algorithms
DLRA	Low-rank training of tensor-structured neural networks
Domain decomposition	Parallel-in-Time algorithm for parabolic optimal control problems On the optimal overlap in Optimized Schwarz Methods under computational cost constraint Domain decomposition dynamical low-rank for multi-dimensional radiative transfer equations
double forms	Two approaches to tensor fields on surfaces
DtN truncation	Wave-number-explicit analysis for maxwell's equation with Dirichlet-to-Neumann truncation
dual weighted residual method	Goal-Oriented Time Adaptivity For Linear pH-DAEs Of Index-1
Dual-Space Kernel Splitting	An O(log N) Monte Carlo method for periodic Coulomb systems
duality	TPDv algorithms for nonlinear PDEs with application to JKO schemes and interface dynamics
dynamic boundary conditions	Coupling Time‑Domain Boundary Integral Equations with Domain Methods or Nonlinear Boundary Dynamics
Dynamic marketing strategies	Optimal control of an innovation diffusion model in Smartphone Markets
dynamic mode decomposition	Heterogeneous Dictionaries Approximate Koopman Invariance: Why Deep Koopman Operators Work
Dynamical low rank method	Dynamical low-rank tensor train approximation for kinetic equations
Dynamical low-rank approximation	Efficient State/Parameter Estimation via Dynamical Low-Rank Kalman Filters Dynamics of two-dimensional dissipative quantum spin systems using tree tensor networks Dynamical Low-Rank Filters for Data Assimilation A Dynamical Low-rank Multilevel Monte Carlo Estimator for High-Dimensional Kinetic Equations Dynamical low-rank approximation of the non-linear Vlasov-Poisson-Fokker-Planck equation for weakly collisional plasmas Robust integrators in computational radiation therapy Combining dynamical low-rank approximation with local refinement strategies for proton radiation therapy Parallel Second-Order Time Integration of Low-Rank Tensors One Step Forward, One Step Back: A Memory-Efficient Dynamical Low-Rank Scheme for the Adjoint State Method Sketch low-rank dynamics: orthogonal vs. oblique projections
dynamical low-rank methods	A scalable hybrid low-rank scheme for thermal radiative transfer
dynamical system	Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model
Dynamical Systems	Data-driven learning of transfer operators using randomized neural networks Neural Networks as a Discretization of Dynamical Systems Using Symplectic Realizations for the Simulation and Learning of Hamiltonian Dynamical Systems Physics-consistent learning of circuit solutions using a topological decoupling of MNA Adaptive momentum and nonlinear damping for neural network training Constructing Macroscopic Dynamics using Deep Learning Building adjoint representations for tomography and compilation Neural Dynamical System with Algebraic Structure Constraint for Compact Geometric Learning
dynamically optimal	Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations
dynamo	Finite element antidynamo theorems and generalized Hodge theory Finite element exterior calculus for spectra and pseudo-spectra of advection-diffusion of differential forms
E
early and long time behaviour	On evolving network models and their influence on opinion formation and control
Earth	Efficient Analysis of Geological Hypotheses using Bayesian Full Waveform Inversion
ECG Image	Multimodal prediction of catheter ablation outcomes in patients with persistent atrial fibrillation
Ecological tipping points	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
Ecosystem resilience	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
Edge element	A Penalty-free Asymmetric Nitsche's Method for Edge Elements
effective models	Transitions in proliferating active matter — particle-based simulations and effective models
Eigenvalue problems	Computing the spectrum of the Schrödinger equation with quasiperiodic potential
Einstein's equations	A polytopal discrete de Rham scheme for Einstein's equations
elasticity	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates Shape and topology optimization for additive manufacturing processes
elastocapillarity	Contact Line Dynamics on Elastic Sheets
electrical treeing	A 3D-1D model of the electrostatic problem on the electrical treeing
Electrodiffusion	CELL-BASED MODELLING AND SIMULATION OF ELECTRICAL AND CHEMICAL INTERPLAY IN EXCITABLE TISSUE
Electronic excited state	A constrained saddle dynamics for computing electronic excited states
Elliptic Equation	Stability of the Second-order Elliptic Equation in Hölder Space and its Application to the PINN Method
Elliptic interface problems	Wavelet Galerkin Methods for the Helmholtz Equation and Elliptic Interface Problems
Elliptic Monge-Ampère equation	A Least-Squares Method for Non-Injective Gradient Mappings via the Mixed Monge-Ampère Equation
Elliptic PDE	Accurate Near-Contact Simulation in 2D Stokes Flow via Two-Body Preconditioning
Energy	An energy and entrophy-conserving enriched Galerkin method for incompressible Navier-Stokes equations Graph-Based Machine Learning Framework for Predicting Hydrogen Storage Capacity in Metal–Organic Frameworks
energy dissipation	High-order parametric local discontinuous Galerkin methods for anisotropic 1 curve-shortening flows An arbitrary Lagrangian--Eulerian sliding interface method for fluid-structure interaction with a rotating rigid structure A Topology Preserving, Energy Dissipative, High-order Lagrangian Finite Element Method for Magnetic Relaxation in Plasma
energy estimate	Error analysis for a finite element discretization of a radially symmetric harmonic map heat flow problem
energy law	A stabilised auxiliary variable approach and its higher order schemes for gradient flows
energy minimization	Energy-Based hp-Adaptivity for the Approximation of Ground States of the Gross–Pitaevskii Equation with Rotation
Energy Network Simulation	Model Hierarchies of Port-Hamiltonian Systems for Efficient Energy Network Simulation
energy stability	Stable fully discrete parametric finite element methods for Willmore flow with applications Energy-stable inertial level-set flow for topology optimization
energy techniques	Time-domain integral equations for the wave equation on moving domains
Energy-conserving scheme	Energy Conserving Semi-Lagrangian Scheme for the Vlasov–Maxwell System
Energy-dissipative systems	Conformal Symplectic Neural Networks for Learning Multiple Energy-Dissipative Systems
energy-preserving scheme	Energy stable auxiliary variable method for Cahn--Hilliard equations
energy-stability	Energy-stable numerical methods for two-phase viscoelastic flows
engineering applications	Numerical Implementation of Fractional Differential Equations for Nonlinear Engineering Systems: Challenges and Considerations
Enriched Galerkin	An energy and entrophy-conserving enriched Galerkin method for incompressible Navier-Stokes equations
Ensemble Kalman Filtering	Efficient State/Parameter Estimation via Dynamical Low-Rank Kalman Filters
Ensemble Prediction	FourCastNet 3: Geometric Neural Operators for Probabilistic Machine Learning Weather Forecast at Scale
ensemble score filter	A Diffusion Model-Based Approach for Uncertainty Reduction in Learning Data-Driven Dynamical Systems
enstrophy	Stabilisation of the Navier⁠–Stokes equations by enstrophy preservation An energy and entrophy-conserving enriched Galerkin method for incompressible Navier-Stokes equations
entropy	A quantitative limit theory for quadratic mean-field controls
entropy conservation	Structure-Preserving Methods for the Compressible Euler Equations
Entropy Stability	An entropy stable well-balanced high order low Mach solver for atmospheric flows
entropy-stable methods	Structure-Preserving Methods for the Compressible Euler Equations
Epstein zeta function	Graph zeta methods for efficient simulations of long-range interacting quantum lattices
equations with memory	High order, variable step approximation of convolution equations
equidistribution principle	Moving sample method for solving time-dependent partial differential equations
ergodic behavior	An explicit ergodicity-preserving fully discrete scheme for the stochastic Burgers--Huxley equation
ergodicity	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds Numerical preservation of measures of ODEs and SDEs with aromatic structures Ergodicity and invariant measure approximation of the stochastic Cahn–Hilliard equation via an explicit fully discrete scheme
error analysis	Parareal for parabolic equations with oscillatory coefficients Error analysis of splitting methods for 3D semilinear wave equations with finite-energy solutions Exponential wave integrators for the Zakharov system Error estimates for a fictitious domain approach in multiphysics interface problems Deterministic and probabilistic rounding error analysis of artificial neural networks in floating-point arithmetic Local Time Integration for Friedrichs’ Systems
Error analysis and regularity assumptions	Rigorous Error Analysis of Symmetric Zassenhaus Splittings in Infinite Dimensions
Error bounds	An oscillation-rewinding splitting method for nonlinear Dirac equations with highly oscillatory solutions Error and Stability Analysis of a Randomized SDIRK Method Error bounds for the truncated Baker-Campbell-Hausdorff formula Time integration of highly-oscillatory, nonlinear Dirac equations Bounding the error of the truncated Magnus expansion for unitary problems
error estimate	Exponential integrator for dispersive equations with concentrated potential
error estimates	Nonequilibrium stochastic dynamics: Error estimates and variance reduction Error estimates for a finite element method for anisotropic mean curvature flow Error estimates for backward difference full discretization of Willmore flow for surfaces A stabilised auxiliary variable approach and its higher order schemes for gradient flows Finite Volume Methods for Stokes Variational Inequalities A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
error estimation	Approximation and Error Bounds for KANs: Applications to Dynamical System Discovery via Linear Multistep Methods
Euler equations	A Discontinuous Galerkin solver as an alternative dynamical core for the ICON model
Euler–Lagrange equations	From fractional variational principles to classical optimization
Evaporating droplets	Variational Modelling and Numerical Simulations for Evaporating Thin Droplets and Coffee-Ring Effect
Event-triggered control	Event-triggered $\mu$-consensus control for nonlinear MASs with unknown-bound delays under stochastic delayed impulses
Evolve-Filter-Relax (EFR) Method	Numerical Analysis of the Evolve-Filter-Relax Reduced Order Model for Buoyancy-Driven Flows
evolving interfaces	Conservative space–time CutFEM for variable surface-tension two-phase flow
evolving surface	A Trace Finite Element Method for a Surface Reaction-Diffusion System Coupled with Surface Motion
Evolving surface finite element method	The two-phase Stefan problem on an evolving surface
evolving surfaces	Strong Stability of Cut Finite Element Methods for Parabolic Problems on Evolving Surfaces
Evovling surface finite element method	Convergence of finite elements for a bulk-surface coupled free boundary problem
EWI	Numerical Investigation of the Schrödinger Equation with Low-Regularity Nonlinearity
exact complexes	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates
Exchange potential	Effective approximations for Hartree-Fock exchange potential
Excitable media	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
Excited States	Fast Algorithms for Full Configuration Interaction
existence	Spherically Symmetric Flow of a Compressible Real Micropolar Gas: Existence, Regularity, and Stabilization
exotic series	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
explicit stabilized methods	Explicit stabilized implementation of singly diagonally implicit Runge-Kutta methods
explicit symmetric schemes	Explicit symmetric low-regularity integrators for the nonlinear Schrodinger equation
explicit tamed scheme	An explicit ergodicity-preserving fully discrete scheme for the stochastic Burgers--Huxley equation
explicit time integrators	Second order explicit stabilized multirate method for stiff differential equations with error control
exponential convergence	Wave-number-explicit analysis for maxwell's equation with Dirichlet-to-Neumann truncation
exponential decay	A Computational Multiscale Method for Heterogeneous Stokes Problems
exponential integrator	A low regularity exponential integrator for the DNLS equation Exponential integrator for dispersive equations with concentrated potential
Exponential integrators	Exploring directional split exponential integrators: from theory to efficient implementation Low-synchronization Arnoldi Algorithms with Application to Exponential Integrators A Magnus-based integrator for Brownian parametric semi-linear oscillators Time integration of highly-oscillatory, nonlinear Dirac equations
Exponential methods	Stiffness resilient exponential integrators
Exponential Nyström integrators	Three New Classes of Exponential Integrators for Stiff and Highly Oscillatory Systems
Exponential Rosenbrock Methods	Exponential Rosenbrock Methods without order reduction when integrating nonlinear initial boundary value problems
Exponential Runge–Kutta methods	Exponential Runge–Kutta methods for parabolic equations with variable delay
Exponential wave integrator	Exponential wave integrators for the Zakharov system
F
f-divergences	Graph-informed GANs: Variational learning with Bayesian network structure
Fast algorithms	A Fast Algorithm for the Fractional Fokker–Planck Equation in Arbitrary Dimensions Accurate Near-Contact Simulation in 2D Stokes Flow via Two-Body Preconditioning
Fast Ewald Summation	Accelerating Fast Ewald Summation with Prolates for Molecular Dynamics Simulations
Fast numerical algorithms	Computationally Efficient Two-Grid ADI Scheme for Two-Dimensional Nonlinear Time-Fractional Reaction–Diffusion Equations
fast solvers for structured linear systems	Solving time fractional ODEs and PDEs.
fast transforms	A sparse spectral method on domains bounded by planar algebraic curves
Fault-tolerant quantum computing	Significantly more efficient Clifford+T synthesis for small-angle rotations and application to Trotterization
FCI	Fast Algorithms for Full Configuration Interaction
Feature Fusion	Multimodal prediction of catheter ablation outcomes in patients with persistent atrial fibrillation
Federated learning	FeDLRT: Federated Dynamical Low-Rank Training
FEEC	Space-time structure preserving discretisation for the wave equation A Topology Preserving, Energy Dissipative, High-order Lagrangian Finite Element Method for Magnetic Relaxation in Plasma
feedback control	A feedback-control perspective on sampling for Langevin and McKean-Vlasov dynamics
FEM	Helicity-preserving finite element schemes for magnetohydrodynamics Positivity-Preserving Finite Element Schemes for SPDEs
FEM-BEM coupling	Coupling Time‑Domain Boundary Integral Equations with Domain Methods or Nonlinear Boundary Dynamics Time dependent acoustic scattering in full space from penetrable objects with nonlinearities
Fermionic wavefunctions	Permutation-structured function estimation via tensor-train sketching
FGMRES	Convergence of flexible GMRES with and without randomized sketching
fictitious domain approach	Efficient and accurate spectral methods for PDEs in complex domains
Fictitious domain method	Error estimates for a fictitious domain approach in multiphysics interface problems
Filippov systems	Discovering Piecewise-Smooth Dynamics from Trajectory Data
filtered integrator	Twice-filtered resonance-based exponential-type integrator (FREI) for the ``good'' Boussinesq equation
finite difference methods	Weighted finite difference methods for a nonlinear Schrödinger equation with highly oscillatory solutions in space and time
finite differences	Intercardinal Splitting Approximations for Kawarada Equations with Cross-Derivative Terms Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations Numerical study of dynamical regimes in the Landau–Lifshitz–Gilbert equation
Finite Element	Firedrake: a differentiable programming framework for finite element simulation Numerical analysis of stochastic subdiffusion problems with fractional noise
finite element approximation	Finite element discretization of nonlinear models of ultrasound heating
Finite Element Discretisation	Model Hierarchies of Port-Hamiltonian Systems for Efficient Energy Network Simulation
finite element exterior calculus	Finite element exterior calculus for time-dependent Hamiltonian partial differential equations Stabilisation of the Navier⁠–Stokes equations by enstrophy preservation Finite element antidynamo theorems and generalized Hodge theory Finite element exterior calculus for spectra and pseudo-spectra of advection-diffusion of differential forms Two approaches to tensor fields on surfaces
Finite element method	Error analysis for a finite element discretization of a radially symmetric harmonic map heat flow problem Error estimates for a fictitious domain approach in multiphysics interface problems Enriching continuous Lagrange finite element approximation spaces using neural networks A unified arbitrary-order Bernstein-Bézier discretization of H(div), H^1 and L^2 for 2D multi-physics problems Finite element scheme for the fractional porous medium equation with fractional pressure A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
Finite element methods	The deal.II finite element library: What it is and how it delivers it Graph Neural Networks for r- and hr-Adaptive Meshing in Finite Element Methods Discontinuous Galerkin Methods for nonlinear wave equations via elliptic regularisation. Stabilising conservative numerical methods with preconditioners
finite element tensor calculus	Two approaches to tensor fields on surfaces
Finite Element Time-domain Methods	Efficient Simulation of Surface Plasmon Polaritons on Complex Graphene Geometries
Finite Elements	High-performance finite element simulations with MFEM Space-time structure preserving discretisation for the wave equation CELL-BASED MODELLING AND SIMULATION OF ELECTRICAL AND CHEMICAL INTERPLAY IN EXCITABLE TISSUE Numerical Approximation of Ginzburg–Landau Energy Minimizers: Finite Elements and Neural Network Approaches
Finite elements in time	Stage-segrated preconditioners for Galerkin time intergrators in Irksome
finite neuron spaces	Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
finite time blow-up	Transverse instability studies for line solitary waves in cubic-quintic nonlinear Schrödinger equations
Finite volume methods	Finite Volume Methods for Stokes Variational Inequalities
Finite-Element Methods	Simulations of Contact-Line Dynamics Using a Novel Lattice-Boltzmann-Finite-Element Method
Finite-time blowup	SIPF-PIC: Efficient Large-Scale Simulation of 3D Chemotactic Systems
finite-time stability	Impulsive Switched Systems with Mixed Dynamics: Lyapunov-Based Analysis of Finite-Time Input-to-State Stability
Firedrake	Learning efficient solvers for time dependent PDEs on the sphere
first-order optimality condition	Analysis of a Phase Field Topology Optimization Problem with Cosserat Continuum and Thermal Dissipation
Fitted mesh	Computationally Efficient Two-Grid ADI Scheme for Two-Dimensional Nonlinear Time-Fractional Reaction–Diffusion Equations
Flash Attention	Hardware aware dynamical low-rank training of large language models
floating-point arithmetic	Deterministic and probabilistic rounding error analysis of artificial neural networks in floating-point arithmetic
Flory-Huggins potential	Overcoming Logarithmic Singularities in the Cahn-Hilliard Equation with Flory-Huggins Potential: An Unconditionally Convergent ADMM Approach
Flow matching	Exploring Statistical and Numerical Designs for Generative Diffusions in Scientific Computing
fluid description of plasma	Structure-preserving solutions of the relativistic moment equations
Fluid dynamics	Learning efficient solvers for time dependent PDEs on the sphere An Entropy-Stable Discontinuous Spectral-Element Method for the Spherical Shallow Water Equation
fluid forecasting	Surrogate Modeling of 3D Rayleigh-Bénard Convection with Equivariant Autoencoders
fluid-structure interaction	An arbitrary Lagrangian--Eulerian sliding interface method for fluid-structure interaction with a rotating rigid structure Modeling and simulation of fluid-structure-contact interaction
flux differencing	Structure-Preserving Methods for the Compressible Euler Equations
fMRI	Learning Image Derived PDE-Phenotypes from fMRI Data
Fokker Planck	Multiscale Inference of Cell Fate Dynamics and Gene Regulatory Networks Under Uncertainty
Fokker--Planck equation	Weak Generative Sampler
Fokker-Planck equation	Positivity-Preserving Deep Density Filters for High-Dimensional SDEs An Adaptive Gaussian-Based Time Integrator for Fokker–Planck Equations
Force Perdiction	Accelerated Machine Learning Atomic Energy and Force Predictions via Fast Kernel Summation
Fourier Spectral Method	Numerical Investigation of the Schrödinger Equation with Low-Regularity Nonlinearity
fractional Brownian motion	Numerical approximations of stochastic time-fractional Burgers equations with fractional Gaussian noise
Fractional calculus	From fractional variational principles to classical optimization A Pontryagin maximum principle for optimal control problems involving generalized distributional-order derivatives Fractional Helmholtz equation Numerical analysis of stochastic subdiffusion problems with fractional noise
Fractional derivative	Numerical approximation for a stochastic Caputo fractional differential equation with multiplicative noise
fractional differential equation	Nonlocal Delay Problems Driven by the Caputo–Fabrizio Operator
fractional differential equations	Numerical issues in variable-order fractional differential equations with piecewise order transitions High order, variable step approximation of convolution equations Solving time fractional ODEs and PDEs. Recent Advances in Spectrally Accurate Collocation Methods for Fractional Modelling Numerical Implementation of Fractional Differential Equations for Nonlinear Engineering Systems: Challenges and Considerations
Fractional Fokker–Planck equation	A Fast Algorithm for the Fractional Fokker–Planck Equation in Arbitrary Dimensions
Fractional HBVMs	Recent Advances in Spectrally Accurate Collocation Methods for Fractional Modelling
fractional Laplacian	Finite element scheme for the fractional porous medium equation with fractional pressure
Fractional Optimal control	A Pontryagin maximum principle for optimal control problems involving generalized distributional-order derivatives
framework	Swamp crossing methods for the canonical polyadic decomposition
Free boundary	Free boundary plasma equilibria with flexible coordinates
Free boundary problem	Convergence of finite elements for a bulk-surface coupled free boundary problem The two-phase Stefan problem on an evolving surface Nonlocal Fisher-KPP Equation with Free Boundaries: Numerical Strategies for Accelerated Spreading and Sensitivity Analysis
Free boundary problems	Cut Finite Element Methods for Curvature‑Driven Interface Evolution
free-energy identification	Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models
Friedrichs' systems	Local Time Integration for Friedrichs’ Systems
front-fixing method	Nonlocal Fisher-KPP Equation with Free Boundaries: Numerical Strategies for Accelerated Spreading and Sensitivity Analysis
front-tracking method	Nonlocal Fisher-KPP Equation with Free Boundaries: Numerical Strategies for Accelerated Spreading and Sensitivity Analysis
frozen-flow	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
Full potential Kohn-Sham DFT	Towards spectral element solutions of full-potential Kohn-Sham equation
fully discrete schemes	Ergodicity and invariant measure approximation of the stochastic Cahn–Hilliard equation via an explicit fully discrete scheme
function approximation	Kernel interpolation in high dimensions with anisotropic sparse grids
Functional data analysis	Functional Data Analysis Using Neural Networks
Functional optimization	A functional approach to differential programming in machine learning
fusion energy	Recent progress, gaps and opportunities in extended-MHD modelling for fusion energy applications
G
Galerkin difference	An implicit geometric particle-in-cell method based on Galerkin difference for the Vlasov-Maxwell system
Galerkin in time	Stage-segrated preconditioners for Galerkin time intergrators in Irksome
GARK	Multirate infinitesimal solutions of DAEs arising in power system simulations
gas emission detection	Leak localisation with a measure source convection–diffusion model
Gaussian convolution inequality	One Integrator Step Is Enough: Adaptive Ensemble Langevin Samplers
Gaussian function	An Adaptive Gaussian-Based Time Integrator for Fokker–Planck Equations
Gaussian kernels	Kernel-based modal regression with right-censored data
Gaussian mixture reduction	An Adaptive Gaussian-Based Time Integrator for Fokker–Planck Equations
Gaussian process emulators	Physics inspired Gaussian processes for Bayesian inverse problems
Gaussian processes	Kernel interpolation in high dimensions with anisotropic sparse grids Towards the Theory of Physics-Informed Gaussian Processes
Gaussian wave packets	Variational Gaussian approximation for the magnetic Schrödinger equation Structure-Preserving Integration for Magnetic Gaussian Wave Packet Dynamics
Gene Regulatory Networks (GRNs)	Multiscale Inference of Cell Fate Dynamics and Gene Regulatory Networks Under Uncertainty
GENE-X	Accelerating Global Gyrokinetic Simulations in GENE-X via Adaptive PIROCK Schemes
generalised continua	Intrinsic $H^{\mathrm{dev}}(\mathrm{Curl})$-conforming elements for planar relaxed micromorphic models
Generalization analysis	Functional Data Analysis Using Neural Networks
Generalization error estimate	Mean-Field Molecular Dynamics Approximation of Quantum Statistical Observables with Machine Learning
generalized convolution quadrature	High order, variable step approximation of convolution equations
generalized Navier slip boundary	A thermodynamically consistent domain embedding model for Cahn-Hilliard-Navier-Stokes equations with generalized Navier-slip boundary conditions
generalized precision	Marginal and conditional independence after diagonal transport
generalized ridge representation	Integrable Splitting for Polynomial Dynamical Systems
Generalized Split Feasibility Problem	Iterative Solutions of Generalized Split Feasibility Problems
Generative adversarial networks	Graph-informed GANs: Variational learning with Bayesian network structure
Generative AI	Generative AI for Uncertainty Quantification and Data Assimilation
Generative diffusions	Exploring Statistical and Numerical Designs for Generative Diffusions in Scientific Computing
generative model	Weak Generative Sampler
Generative modeling	Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations Scientific Data Reduction Methods
generative modelling	Lipschitz-regularized gradient flows and generative particle algorithms
Generative Models	AI and Molecular Dynamics: a theoretical perspective on why generative models can boost sampling Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems
geometric deep learning	Surrogate Modeling of 3D Rayleigh-Bénard Convection with Equivariant Autoencoders
Geometric discretisation	On the relation of direct and indirect approaches for unconstrained optimal control problems
geometric flows	High-order parametric local discontinuous Galerkin methods for anisotropic 1 curve-shortening flows A Minimal-Deformation-Rate Framework for Surface Evolution: From Curvature Flows to Shape Optimization Arbitrary-order structure-preserving discretizations for geometric curvature flows
Geometric hydrodynamics	Geometric regularisation of two-dimensional turbulence Backward Error Analysis of Isospectral Integrators via Lie–Poisson Reduction of Butcher Series
Geometric integration	Approximating the Matrix Exponential for Large Time Steps An exponential-free structure preserving integrator for stochastic Lie-Poisson systems
geometric integrators	Quadratic projectable Runge-Kutta methods
Geometric Machine Learning	FourCastNet 3: Geometric Neural Operators for Probabilistic Machine Learning Weather Forecast at Scale Neural Dynamical System with Algebraic Structure Constraint for Compact Geometric Learning
Geometric multigrid	Stabilising conservative numerical methods with preconditioners
geometric nonlinearities	Numerical Analysis of Nonlinear Beam Networks
geometric numerical integration	Geometric Adjoint Sensitivity Analysis and Hamiltonian Variational Integrators Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds Structure-preserving low-regularity integrators for dispersive nonlinear equations A Hierarchical Splitting Approach for N-Split Differential Equations Integrable Splitting for Polynomial Dynamical Systems
Geometric PDEs	Arbitrary Lagrangian–Eulerian Schemes for Moving Interface Problems
geometrical optics	Inverse methods for optical design
Geometrically explicit modelling	CELL-BASED MODELLING AND SIMULATION OF ELECTRICAL AND CHEMICAL INTERPLAY IN EXCITABLE TISSUE
Geometry	Finite element discretization of Yang–Mills connections
geophysical flows	A numerical investigation of the Hopf bifurcation occurring in quasi-geostrophic channel flow
Geophysical fluid dynamics	Fully implicit timestepping methods for the rotating shallow water equations
Gibbs Measure	A qualitative study of the reflected Kinetic Langevin process
Ginzburg--Landau dynamics	Hybrid quantum-classical algorithms for complex nonlinear partial differential equations with Ginzburg-Landau potential and vortex motion laws
Ginzburg-Landau model	Numerical Approximation of Ginzburg–Landau Energy Minimizers: Finite Elements and Neural Network Approaches
Girsanov's theorem	Efficient computation of transport coefficients using the Green–Kubo formula with Girsanov’s reweighting
global optimization	Global optimization in very rugged landscapes for a kinetic beam heating problem
GMRES	Convergence of flexible GMRES with and without randomized sketching
goal-oriented	Goal-Oriented Low-Rank Tensor Decompositions for Numerical Simulation Data
Goemetric Integration	Structure preservation and Deep Learning for Learning Mechanical Systems from Data
Good Boussinesq equation	Twice-filtered resonance-based exponential-type integrator (FREI) for the ``good'' Boussinesq equation
GPU	High-performance finite element simulations with MFEM
graded meshes	High order, variable step approximation of convolution equations
Gradient Curse	Accelerated Machine Learning Atomic Energy and Force Predictions via Fast Kernel Summation
Gradient flow	A kernel approach for the learning of Wasserstein geometric flows A Topology Preserving, Energy Dissipative, High-order Lagrangian Finite Element Method for Magnetic Relaxation in Plasma
gradient flows	Lipschitz-regularized gradient flows and generative particle algorithms A stabilised auxiliary variable approach and its higher order schemes for gradient flows Energy-Based hp-Adaptivity for the Approximation of Ground States of the Gross–Pitaevskii Equation with Rotation
Gradient Free	Efficient Derivative-Free Bayesian Inference for Large-Scale Inverse Problems
gradient-descent-free training	Rapid training of Hamiltonian Graph Networks using random features
Gram-Schmidt	Low-synchronization Arnoldi Algorithms with Application to Exponential Integrators
Gramian	Computing Cholesky-factors of finite-horizon Gramians
Graph neural networks	Graph Neural Networks for r- and hr-Adaptive Meshing in Finite Element Methods Rapid training of Hamiltonian Graph Networks using random features
Graph Nueral Networks	Stuart-Landau Oscillatory Graph Neural Network
graph signal processing	Conjugate Phase Retrieval on Graphs and with Applications to the Shift-Invariant Spaces
Graph theory	Graph-Based Machine Learning Framework for Predicting Hydrogen Storage Capacity in Metal–Organic Frameworks
Graphene	Quantum Elastic Network Models and their Application to Graphene Efficient Simulation of Surface Plasmon Polaritons on Complex Graphene Geometries
graphons	Learning graphons from data: Random walks, transfer operators, and spectral clustering
greedy methods	Approximating distributions through greedy mixtures: an algorithmic framework.
Green function	Learning Green's functions from data
Green--Kubo	Efficient computation of transport coefficients using the Green–Kubo formula with Girsanov’s reweighting
grid-free optimisation approach	Leak localisation with a measure source convection–diffusion model
Gross-Pitaevskii equation	Numerical simulation of the Gross–Pitaevskii and magnetic Ginzburg-Landau equation via vortex tracking
Gross–Pitaevskii	Energy-Based hp-Adaptivity for the Approximation of Ground States of the Gross–Pitaevskii Equation with Rotation
ground-state search	Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
Group equivariance	Geometric PDE-based Neural Networks for Image Processing
Gyrokinetic plasma simulations	Accelerating Global Gyrokinetic Simulations in GENE-X via Adaptive PIROCK Schemes
H
h-Adaptive mesh methods	Towards spectral element solutions of full-potential Kohn-Sham equation
Hagedorn wavepacket	Vibrationally resolved electronic spectra from Hagedorn wavepacket dynamics
half-densities	Vakonomic Fluids
Hallucinations	Necessary mechanisms for super AI and stopping hallucinations: The consistent reasoning paradox and the indeterminacy function
Hamilton-Jacobi equation	Energy-stable inertial level-set flow for topology optimization
Hamiltonian flow	Learning Hamiltonian PDEs
Hamiltonian model	Reentrance in a Hamiltonian flocking model
Hamiltonian neural network	Rapid training of Hamiltonian Graph Networks using random features
Hamiltonian partial differential equations	Symplectic Spectral Neural Operators for Non-canonical Hamiltonian PDEs
Hamiltonian PDEs	Geometric Property of the Brinkman Penalization Method for Hamiltonian PDEs and Its Applications Learning Hamiltonian PDEs Stabilising conservative numerical methods with preconditioners
Hamiltonian simulation	Hamiltonian Simulation with Magnus Expansion Nearly optimal quantum simulation of slow time-dependent Hamiltonians
Hamiltonian structure	Structure preservation in plasmas via matrix hydrodynamics
Hamiltonian System	Numerical simulation of the Gross–Pitaevskii and magnetic Ginzburg-Landau equation via vortex tracking Nonlinear Variational Integrators
Hamiltonian systems	Symplectic Neural Operator for Learning Hamiltonian PDEs A kernel approach for the learning of Wasserstein geometric flows Sparse identification of port-Hamiltonian systems from noisy data Integrable Splitting for Polynomial Dynamical Systems
hard spheres	Computational geometry of active matter: Space to insert hard spheres
harmonic map heat flow	Error analysis for a finite element discretization of a radially symmetric harmonic map heat flow problem
harmonic map heat flows	A Second-order Structure-preserving Parametric FEM for Surface Evolution
Hartree-Fock	Geometric methods for electronic dynamics and excited-state calculations Effective approximations for Hartree-Fock exchange potential
Hartree–Fock	The Witten Laplacian on Riemannian Manifolds: Computational Methods for Saddle-Point Problems
Hele-Shaw problem	Dynamics of Hele-Shaw flow in Multi-connected Regions
Hellinger-Reissner	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates
Helmholtz equations	Wavelet Galerkin Methods for the Helmholtz Equation and Elliptic Interface Problems
Herglotz's variational principle	Discrete Contact Mechanics from the Herglotz Variational Principle
Heun method	Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
Hierarchical	Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
high accuracy	Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation
High dimension	A Deep Neural Network for Pricing American Options under Jump-Diffusion in High Dimension: A Backward Stochastic Differential Equation Approach
high dimensional approximation	Kernel interpolation in high dimensions with anisotropic sparse grids
High dimensional problems	On Tackling High-Dimensional Nonconvex Optimization via Stochastic First-Order Methods
High order methods	An entropy stable well-balanced high order low Mach solver for atmospheric flows
High order scheme	A fully-decoupled second-order-in-time and unconditionally energy stable scheme for the moving contact line problem
high order schemes	A stabilised auxiliary variable approach and its higher order schemes for gradient flows
high performance computing	Exploring directional split exponential integrators: from theory to efficient implementation Sketch low-rank dynamics: orthogonal vs. oblique projections
High Performance Implementations	Accelerating Fast Ewald Summation with Prolates for Molecular Dynamics Simulations
High-dimensional	Positivity-Preserving Deep Density Filters for High-Dimensional SDEs
high-dimensional advection-diffusion equations	Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
high-dimensional integrals	Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation
High-dimensional nonlinear problems	Computationally Efficient Two-Grid ADI Scheme for Two-Dimensional Nonlinear Time-Fractional Reaction–Diffusion Equations
High-dimensional PDEs	A Fast Algorithm for the Fractional Fokker–Planck Equation in Arbitrary Dimensions Parallel Second-Order Time Integration of Low-Rank Tensors
High-dimensional simulations	Scalability of high-dimensional Vlasov-Poisson simulations with communication-avoiding asynchronous discontinuous Galerkin
high-dimensional statistics	Permutation-structured function estimation via tensor-train sketching
High-dimensional stochastic systems	Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems
high-frequency oscillations	Weighted finite difference methods for a nonlinear Schrödinger equation with highly oscillatory solutions in space and time
high-frequency wave propagation	Analytical Approximation of Nonlinear Friedrichs Systems by Modulated Fourier Expansions
High-order	Stage-segrated preconditioners for Galerkin time intergrators in Irksome
high-order accuracy	High-order parametric local discontinuous Galerkin methods for anisotropic 1 curve-shortening flows
High-Performance Computing	A scalable hybrid low-rank scheme for thermal radiative transfer Generative AI for Uncertainty Quantification and Data Assimilation
higher-order methods	Centrifuged convection in an enclosed cube: boundary layer structures
higher-order tensors	Swamp crossing methods for the canonical polyadic decomposition
highly concentrated potential	Exponential integrator for dispersive equations with concentrated potential
highly oscillatory	Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations
highly oscillatory problems	An oscillation-rewinding splitting method for nonlinear Dirac equations with highly oscillatory solutions Time integration of highly-oscillatory, nonlinear Dirac equations
highly oscillatory Stokes problem	A Computational Multiscale Method for Heterogeneous Stokes Problems
Hilbert Space	Iterative Solutions of Generalized Split Feasibility Problems
Hilbert transform	High-Precision Hilbert Transform from Discrete Uniform Samples: Extracting Non-Integer Algebraic Decay Orders via the Matrix Pencil Method
HIV-AIDS	Modeling and optimal control of SICA epidemic models
Hodge theory	Finite element antidynamo theorems and generalized Hodge theory
Hodge wave equation	Finite element exterior calculus for time-dependent Hamiltonian partial differential equations
Homogeneous spaces	Noise and stochastic processes on homogeneous spaces
Hopf algebra	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
hp-adaptive FEM	Energy-Based hp-Adaptivity for the Approximation of Ground States of the Gross–Pitaevskii Equation with Rotation
hp-FEM	hp-FEM for Maxwell’s equations in piecewise smooth media
HPC	High-performance finite element simulations with MFEM Extreme Scaling of a 1.5km global weather and climate model
HSS	Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
Hu-Zhang elements	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates
hybrid block	A Family of High Order Second Derivative Hybrid Block Methods for The Numerical Integration of Stiff Initial Value Problems in Ordinary Differential Equations
hybrid quantum--classical methods	Hybrid quantum-classical algorithms for complex nonlinear partial differential equations with Ginzburg-Landau potential and vortex motion laws
Hybrid quantum-classical	Integrating Quantum Algorithms Into Classical Frameworks
Hybrid Surrogate Models	A Variational Framework for the Algorithmic Complexity of PDEs
Hybridization	Finite element exterior calculus for time-dependent Hamiltonian partial differential equations
Hydrogen	Graph-Based Machine Learning Framework for Predicting Hydrogen Storage Capacity in Metal–Organic Frameworks
Hyperbolic Monge-Ampère equation	A Least-Squares Method for Non-Injective Gradient Mappings via the Mixed Monge-Ampère Equation
Hyperplane Arrangements	Detecting unargmaxable outputs in low-rank classifiers
hypocoercivity	Convergence of the two-timescale gradient descent-ascent algorithm
I
ILES	Evaluating Global Scale Numerics on Small Scale Flows
image classifiers	Low Rank Affine Adversarial Attacks on Image Classifiers
Image processing	Geometric PDE-based Neural Networks for Image Processing
Imaging	Efficient Analysis of Geological Hypotheses using Bayesian Full Waveform Inversion
imaging inverse problems	Fast Unsupervised Training of Deep Inverse Models
ImEx	Order Reduction in Implicit-Explicit Runge-Kutta methods, and ways to overcome it A IMEX-based spectral scheme with adaptive time-stepping for the Vlasov-Poisson system in the quasi-neutral limit
IMEX Runge-Kutta time integration	A Discontinuous Galerkin solver as an alternative dynamical core for the ICON model
IMEX time integration	Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
Immersed Boundary Method	Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
Implicit Runge-Kutta methods	Fully implicit timestepping methods for the rotating shallow water equations Extended Krylov method for fully implicit Runge-Kutta methods Explicit stabilized implementation of singly diagonally implicit Runge-Kutta methods
implicit-explicit	Runge-Kutta methods for Nonlinearly Partitioned Equations
implicit-implicit	Runge-Kutta methods for Nonlinearly Partitioned Equations
Importance sampling	Importance sampling for Adaptive Multilevel Splitting Posterior Regression ImpOrtance Reweighting (PRIOR) Efficient computation of transport coefficients using the Green–Kubo formula with Girsanov’s reweighting
incompressible Euler flow	Vakonomic Fluids
incompressible flow	A Priori and a Posteriori Error Estimate for Pressure Robust Schemes for Incompressible Flow
incompressible Navier–Stokes equations	Stabilisation of the Navier⁠–Stokes equations by enstrophy preservation
incompressible viscous flow	Higher-order unfitted FEM for Stokes with strongly divergence-free velocity up to the boundary
Indeterminacy function	Necessary mechanisms for super AI and stopping hallucinations: The consistent reasoning paradox and the indeterminacy function
index-1 saddle points	The Witten Laplacian on Riemannian Manifolds: Computational Methods for Saddle-Point Problems
inertial level-set flow	Energy-stable inertial level-set flow for topology optimization
Infinite-dimensional Learning Theory	Statistical Frameworks for Learning Nonlinear Mappings in Infinite Dimensions
Infinite-dimensional operators	Rigorous Error Analysis of Symmetric Zassenhaus Splittings in Infinite Dimensions
Infinitesimal generator	Convergence speed in distribution of finite particle systems to McKean-Vlasov-type equations using generators of measure-valued diffusions
Information-Theoretic Optimization	Information-Theoretic Learnable Conformal Prediction for Flexible Uncertainty Calibration in MLIPs
initial-boundary value problems	Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables
Innovation diffusion	Optimal control of an innovation diffusion model in Smartphone Markets
input-to-state stability	Impulsive Switched Systems with Mixed Dynamics: Lyapunov-Based Analysis of Finite-Time Input-to-State Stability
integrability	From explicit formulas to Wave Kinetic theory for the Benjamin–Ono equation
integral equations	Fast evaluation of layer and volume potentials for the modified Helmholtz equation Simple and Efficient Discretization of Integral Operators on Deformed Spheres
Integral Operator	Fractional Helmholtz equation
Integral probability metrics	Graph-informed GANs: Variational learning with Bayesian network structure
integral representation	Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
integro-differential equations	Solving time fractional ODEs and PDEs. An Isogeometric Collocation Framework for Neural Field Models on Multi-Patch NURBS Surfaces
Interacting Particle dynamics	Non mean field Vicsek type models for collective behaviour:
interacting particle systems	A feedback-control perspective on sampling for Langevin and McKean-Vlasov dynamics Data-driven approximation of transfer operators for mean-field stochastic differential equations Coarse-Grained Modeling of Clustering Dynamics in Interacting Particle Systems A discontinuous Galerkin method for the Dean-Kawasaki equation
interface problem	A Cartesian Grid-based Boundary Integral Method for Acoustic Scattering
Interface problems	Cut Finite Element Methods for Curvature‑Driven Interface Evolution Error estimates for a fictitious domain approach in multiphysics interface problems
Interfacial Dynamics	Simulations of Contact-Line Dynamics Using a Novel Lattice-Boltzmann-Finite-Element Method
interpolatory low-rank schemes	A scalable hybrid low-rank scheme for thermal radiative transfer
intrinsic dimension	Kernel-based modal regression with right-censored data
invariant distribution sampling	Weak Generative Sampler
inverse conductivity problem	A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
inverse modeling	Heterogeneous Dictionaries Approximate Koopman Invariance: Why Deep Koopman Operators Work
Inverse problem	Free boundary plasma equilibria with flexible coordinates
Inverse Problems	Inexact Algorithms for Bilevel Learning Posterior Regression ImpOrtance Reweighting (PRIOR) Neural network surrogates with uncertainty quantification for inverse problems in PDEs Approximating distributions through greedy mixtures: an algorithmic framework. Physics inspired Gaussian processes for Bayesian inverse problems Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models Enhancing Full Waveform Inversion and Least-Squares Reverse Time Migration via Learned and Regularized Source Wavelet Manipulation Learning Physics Directly From Corrupted Data.
Inversion	Efficient Analysis of Geological Hypotheses using Bayesian Full Waveform Inversion
isentropic Euler system	A Real Gas Spherically Symmetric Euler Framework with Self Gravity for Modelling Stellar Structure and Collapse
Isogeometric collocation	An Isogeometric Collocation Framework for Neural Field Models on Multi-Patch NURBS Surfaces
Isoparametric Higher Order Method	Higher Order Unfitted Space-Time Finite Element Methods
Isospectral equations	Backward Error Analysis of Isospectral Integrators via Lie–Poisson Reduction of Butcher Series
isospectral Lie-Poisson flows	Geometric low-rank approximation of the Zeitlin model of incompressible fluids on the sphere
Iterative least-squares method	A Least-Squares Method for Non-Injective Gradient Mappings via the Mixed Monge-Ampère Equation
Iterative methods	TPDv algorithms for nonlinear PDEs with application to JKO schemes and interface dynamics Extended Krylov method for fully implicit Runge-Kutta methods Stage-segrated preconditioners for Galerkin time intergrators in Irksome
iterative thresholding，	A Multiscale Hierarchical Segmentation Framework for Cell Fluorescence Microscopy
J
JKO schemes	TPDv algorithms for nonlinear PDEs with application to JKO schemes and interface dynamics
Jump diffusion model	A Deep Neural Network for Pricing American Options under Jump-Diffusion in High Dimension: A Backward Stochastic Differential Equation Approach
K
Kalman inversion	Efficient Derivative-Free Bayesian Inference for Large-Scale Inverse Problems
Kernel Approximations	Efficient molecular dynamics simulations for confined systems: kernel approximations & random batch sampling
kernel methods	Kernel methods for differential equations: high-dimensional and physics-informed settings A kernel approach for the learning of Wasserstein geometric flows Learning Green's functions from data From Koopman to polynomial embeddings for data-driven learning of nonlinear dynamics
Kernel Summation	Accelerated Machine Learning Atomic Energy and Force Predictions via Fast Kernel Summation
kernels	Kernel interpolation in high dimensions with anisotropic sparse grids
Kinetic	A IMEX-based spectral scheme with adaptive time-stepping for the Vlasov-Poisson system in the quasi-neutral limit
kinetic energy preservation	Structure-Preserving Methods for the Compressible Euler Equations
kinetic equation	Global optimization in very rugged landscapes for a kinetic beam heating problem
Kinetic equations	Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Adjoint Monte Carlo Simulation of Kinetic Equations with Reversible Random Number Generators A scalable hybrid low-rank scheme for thermal radiative transfer A Dynamical Low-rank Multilevel Monte Carlo Estimator for High-Dimensional Kinetic Equations Dynamical low-rank tensor train approximation for kinetic equations Combining dynamical low-rank approximation with local refinement strategies for proton radiation therapy Domain decomposition dynamical low-rank for multi-dimensional radiative transfer equations
Kinetic Langevin	A qualitative study of the reflected Kinetic Langevin process
Kinetic Langevin dynamics	One Integrator Step Is Enough: Adaptive Ensemble Langevin Samplers
kinetic Langevin sampler	Long-time behaviour of kinetic Langevin sampler
Kinetic Modeling	Consistent Projection of Langevin Dynamics: Preserving Thermodynamics and Kinetics in Coarse-Grained Models
Kinetic models	Multi-fidelity and multi-level Monte Carlo methods for kinetic models of traffic flow
kinetic PDEs	Non mean field Vicsek type models for collective behaviour:
kinetic simulation	A tensor train numerical approach for Boltzmann equation
Kirchhoff Love	Unified numerical analysis for thermoelastic diffusion and thermo-poroelasticity of thin plates
Kolmogorov-Arnold network	Approximation and Error Bounds for KANs: Applications to Dynamical System Discovery via Linear Multistep Methods
Koopman operator	Learning dynamical systems from data: Gradient-based dictionary optimization Preserving Transition Rates in Coarse-grained Models with Koopman Methods From Koopman to polynomial embeddings for data-driven learning of nonlinear dynamics
Koopman operators	Heterogeneous Dictionaries Approximate Koopman Invariance: Why Deep Koopman Operators Work
Koopman representation	Vakonomic Fluids
Kronecker sum structure	Exploring directional split exponential integrators: from theory to efficient implementation
Krylov methods	Low-synchronization Arnoldi Algorithms with Application to Exponential Integrators Extended Krylov method for fully implicit Runge-Kutta methods
Krylov subspace	Convergence of flexible GMRES with and without randomized sketching
Kuznetsov's equation	Finite element discretization of nonlinear models of ultrasound heating
Kähler dynamics	Geometric methods for electronic dynamics and excited-state calculations
L
L1 scheme	Numerical analysis of stochastic subdiffusion problems with fractional noise
Lagrange multiplier	Error estimates for a fictitious domain approach in multiphysics interface problems
lagrangian	Neural non-canonical Hamiltonian dynamics for long-time simulations
Lagrangian code	The Parker Problem - An Update
Lagrangian coherent structures	Transport and mixing in fluid flows: a network-based approach
Lagrangian method	A Topology Preserving, Energy Dissipative, High-order Lagrangian Finite Element Method for Magnetic Relaxation in Plasma
Laguerre spectral method	An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
Landau equation	Particle Methods for Plasma Equations
Landau–Lifshitz–Gilbert equation	Numerical study of dynamical regimes in the Landau–Lifshitz–Gilbert equation
Langevin	Langevin Monte Carlo methods for Bayesian inference
Langevin diffusion	Velocity jumps for faster molecular dynamics simulations
Langevin diffusions	Noise and stochastic processes on homogeneous spaces Splitting methods for momentum Langevin diffusions on Lie groups of compact type
Langevin dynamics	Langevin sampling methods with adaptive friction and stepsize A feedback-control perspective on sampling for Langevin and McKean-Vlasov dynamics Numerical methods for constraint Langevin dynamics with complex heat bath models
Laplace transform	Numerical issues in variable-order fractional differential equations with piecewise order transitions
Laplacian eigenfunction	Laplacian Eigenfunction-Based Neural Operator for Learning Nonlinear Reaction–Diffusion Dynamics
Large Language Models	Adaptive momentum and nonlinear damping for neural network training
large scale computing	mdBFGS: a Diagonal BFGS Method with Momentum for Stochastic Optimisation
large wave number	Wave-number-explicit analysis for maxwell's equation with Dirichlet-to-Neumann truncation
Large-scale systems	Convergence analysis for a full discretization of operator-valued differential Riccati equations
Latent Attention	Hardware aware dynamical low-rank training of large language models
Latent space	Variational data assimilation in the latent space of an implicit-rank-minimising autoencoder
Latent state-space modeling	Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems
Lattice Boltzmann method	An end-to-end quantum algorithm for nonlinear fluid dynamics with bounded quantum advantage
Lattice-Boltzmann Method	Simulations of Contact-Line Dynamics Using a Novel Lattice-Boltzmann-Finite-Element Method
Laudau equation	Energy-Dissipative and Conservative Discrete Gradient Particle Methods for Aggregation-Diffusion Equations and the Landau Equation
law of large numbers	Ergodicity and invariant measure approximation of the stochastic Cahn–Hilliard equation via an explicit fully discrete scheme
layer-wise approximation rates	Multigrade Neural Network Approximation and Layer-wise Geometric Rates
Learnable Conformal Prediction	Information-Theoretic Learnable Conformal Prediction for Flexible Uncertainty Calibration in MLIPs
learned splittings	Approximating the Matrix Exponential for Large Time Steps
Learning mechanical systems	Structure preservation and Deep Learning for Learning Mechanical Systems from Data
learning rates	Kernel-based modal regression with right-censored data
Learning theory	Unbounded Density Ratio Estimation and Its Application to Covariate Shift Adaptation Kernel-based modal regression with right-censored data
least-squares method	Inverse methods for optical design Convergence and error estimates for P_1 finite element method for the Monge-Ampère equation
Least-Squares Reverse Time Migration	Enhancing Full Waveform Inversion and Least-Squares Reverse Time Migration via Learned and Regularized Source Wavelet Manipulation
LFRic	Extreme Scaling of a 1.5km global weather and climate model
Lie group Lie algebra	Neural Dynamical System with Algebraic Structure Constraint for Compact Geometric Learning
Lie groups	Splitting methods for momentum Langevin diffusions on Lie groups of compact type
Lie-group methods	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
Lie-Poisson integrators	Structure preservation in plasmas via matrix hydrodynamics
Lie-Poisson reduction	Backward Error Analysis of Isospectral Integrators via Lie–Poisson Reduction of Butcher Series
Lie-Trotter splitting	On splitting strategies for the numerical solution of stochastic delay differential equations with correlated noises
Lie–Poisson systems	An exponential-free structure preserving integrator for stochastic Lie-Poisson systems
Lindblad equation	Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations
Linear combination of Hamiltonian simulation	Schrödingerization for quantum linear systems problems with near-optimal dependence on matrix queries
linear elasticity	Analysis of a Phase Field Topology Optimization Problem with Cosserat Continuum and Thermal Dissipation
linear multistep method	Approximation and Error Bounds for KANs: Applications to Dynamical System Discovery via Linear Multistep Methods
Linear PDEs	Towards the Theory of Physics-Informed Gaussian Processes
Linear Programming	Detecting unargmaxable outputs in low-rank classifiers
Linear system	Convergence of flexible GMRES with and without randomized sketching
Linearly implicit	Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
Linearly implicit time integrators	Problem-oriented W-methods for advection-diffusion-reaction PDEs arising in vegetation dynamics
Lipid Raft Patterning	A Thermodynamically Consistent Bulk-Surface PDE Model for Morphogen-Driven Receptor Dynamics and Lipid Raft Patterning
Lipschitz estimate	Wasserstein Bounds for generative diffusion models with Gaussian tail targets
Lipschitz regularisation	Lipschitz-regularized gradient flows and generative particle algorithms
Local adaptive space–time refinement	Adaptive Minimal Residual Methods for Parabolic Problems on Locally Refined Space-Time Meshes
Local discontinuous Galerkin method	High-order parametric local discontinuous Galerkin methods for anisotropic 1 curve-shortening flows
Local refinement	Combining dynamical low-rank approximation with local refinement strategies for proton radiation therapy
local time-integration	Local Time Integration for Friedrichs’ Systems
local time-stepping	Second order explicit stabilized multirate method for stiff differential equations with error control
Localized Orthogonal Decomposition	Quantum Enhanced Numerical Homogenization
locking	Locking-free shells with structure-preserving mixed finite elements
Long-range convolution	LSR-Net: Long-Short-Range Operator Learning for Pattern Dynamics on Manifolds
Long-Range Electrostatics	An O(log N) Monte Carlo method for periodic Coulomb systems
Long-range interactions	Dynamics of two-dimensional dissipative quantum spin systems using tree tensor networks Machine-Learning Interatomic Potentials for Long-Range Systems
Loss of derivatives	Exponential wave integrators for the Zakharov system
low	Global space-time low-complexity numerical methods for the time-dependent Schrödinger equation
Low fidelity models	Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations
Low Mach	An entropy stable well-balanced high order low Mach solver for atmospheric flows
low rank	Dynamical Low-Ranking Compression of Neural Networks with Robustness Under Adversarial Attacks Incremental Tensor-Train Reduced Basis Construction from Sequential Low-Rank Snapshots
Low rank approximation	FeDLRT: Federated Dynamical Low-Rank Training
low rank transformations	Low Rank Affine Adversarial Attacks on Image Classifiers
low regularity	A low regularity exponential integrator for the DNLS equation Explicit symmetric low-regularity integrators for the nonlinear Schrodinger equation Numerical Investigation of the Schrödinger Equation with Low-Regularity Nonlinearity
low regularity integrator	Low-regularity integrators for nonlinear dispersive equations via continuous formulations of numerical schemes
low regularity potential and nonlinearity	Computational methods for the nonlinear Schroedinger equation with low regularity potential and nonlinearity
Low-rank	Hardware aware dynamical low-rank training of large language models Low-rank training of tensor-structured neural networks Low-Rank Anderson Acceleration for Nonlinear Matrix and Tensor Equations Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
Low-rank approximation	Geometric low-rank approximation of the Zeitlin model of incompressible fluids on the sphere Domain decomposition dynamical low-rank for multi-dimensional radiative transfer equations Effective approximations for Hartree-Fock exchange potential
Low-Rank Factorization	Improved Global Landscape Guarantees for Low-rank Factorization in Synchronization Low-rank factorization for music audio signals analysis
Low-rank methods	Convergence analysis for a full discretization of operator-valued differential Riccati equations
low-rank representation	A Nonlinear Tensor Network Architecture for Compressed End-to-End Learning
Low-rank tensor methods	Geometric methods for electronic dynamics and excited-state calculations
low-rank tensor product methods	Low-Rank Tensor Product Approximations for the Radiative Transfer Equation in Plane-Parallel Geometry
low-regularity error estimates	Twice-filtered resonance-based exponential-type integrator (FREI) for the ``good'' Boussinesq equation
Low-regularity integration	Structure-preserving low-regularity integrators for dispersive nonlinear equations
Low-regularity problems	Error and Stability Analysis of a Randomized SDIRK Method
Low-storage methods	Doubling for Splitting
Lower bounds	Quantum algorithms and lower bounds for differential equations
Lubrication and wall effects	Slender-body theory-like approaches for fibres by walls in slow viscous flow
Lyapunov function	Computer-Assisted Search for Differential Equations Corresponding to Optimization Methods and Their Convergence Rates
M
Machine learning	Efficient Sensitivity Analysis for Systems with Multiple Time Scales or Fidelities Neural non-canonical Hamiltonian dynamics for long-time simulations Inexact Algorithms for Bilevel Learning Accurate and robust analysis of molecular kinetics with random features AI weather forecasting: Past, present and future A Diffusion Model-Based Approach for Uncertainty Reduction in Learning Data-Driven Dynamical Systems Dynamical Low-Ranking Compression of Neural Networks with Robustness Under Adversarial Attacks Using Symplectic Realizations for the Simulation and Learning of Hamiltonian Dynamical Systems Preserving Transition Rates in Coarse-grained Models with Koopman Methods Machine-learned coarse-graining for everything and everyone Learning efficient solvers for time dependent PDEs on the sphere Machine Learning-Enhanced Multigrid for Convection-Dominated Flows FeDLRT: Federated Dynamical Low-Rank Training Learning Hamiltonian PDEs Reducing Requirements on Data by Incorporating Structure Constructing Macroscopic Dynamics using Deep Learning Accelerating SAV-based optimisation via randomised low-rank Hessian approximation Learning Physics Directly From Corrupted Data. Graph-Based Machine Learning Framework for Predicting Hydrogen Storage Capacity in Metal–Organic Frameworks Accelerated Machine Learning Atomic Energy and Force Predictions via Fast Kernel Summation
Machine learning and AI	Physics-consistent learning of circuit solutions using a topological decoupling of MNA
Machine Learning Potentials	Coarse-Grained Molecular Sampling with Machine Learning
Machine-Learned Interatomic Potentials	Information-Theoretic Learnable Conformal Prediction for Flexible Uncertainty Calibration in MLIPs
Machine-learning interatomic potentials	Machine-Learning Interatomic Potentials for Long-Range Systems
magnetic Ginzburg-Landau equation	Numerical simulation of the Gross–Pitaevskii and magnetic Ginzburg-Landau equation via vortex tracking
Magnetic Relaxation	Structure-preserving Magnetic Relaxation in Stellarator Geometries A Topology Preserving, Energy Dissipative, High-order Lagrangian Finite Element Method for Magnetic Relaxation in Plasma
magnetic Schroedinger equation	Structure-Preserving Integration for Magnetic Gaussian Wave Packet Dynamics
magneto-friction	The limitations of magneto-frictional relaxation
magnetohydrodynamics	Structure-preserving Magnetic Relaxation in Stellarator Geometries The limitations of magneto-frictional relaxation The Parker Problem - An Update Finite element antidynamo theorems and generalized Hodge theory Recent progress, gaps and opportunities in extended-MHD modelling for fusion energy applications A Curvilinear Lagrangian discontinuous Galerkin method for resistive magneto-hydrodynamics
Magnetostatics	Magnetostatic scattering from axisymmetric open surfaces
Magnus expansion	Hamiltonian Simulation with Magnus Expansion Bounding the error of the truncated Magnus expansion for unitary problems
Magnus expansions	A Magnus-based integrator for Brownian parametric semi-linear oscillators
Manifold Optimisation	Neural Dynamical System with Algebraic Structure Constraint for Compact Geometric Learning
Markov chain Monte Carlo	Langevin sampling methods with adaptive friction and stepsize Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling The unconventional Hug integrator One Integrator Step Is Enough: Adaptive Ensemble Langevin Samplers
Markov processes	Accurate and robust analysis of molecular kinetics with random features
Markov properties	Marginal and conditional independence after diagonal transport
Markovian approximate dynamics	Markovian Approximation for Nonlinear Overdamped Langevin Systems
mass conservation	A Priori and a Posteriori Error Estimate for Pressure Robust Schemes for Incompressible Flow Conservative space–time CutFEM for variable surface-tension two-phase flow
Mass preservation	Nonstandard Finite Difference and Modified Patankar Schemes
Massively parallel	Low-synchronization Arnoldi Algorithms with Application to Exponential Integrators
Materials science	Computing the spectrum of the Schrödinger equation with quasiperiodic potential
mathematical ecology	Geometric analysis of an epidemiological model for Olive Quick Decline Syndrome (OQDS)
Mathematical modeling	Modeling and optimal control of SICA epidemic models
Mathematical software	The deal.II finite element library: What it is and how it delivers it
Matrix exponential	Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling Approximating the Matrix Exponential for Large Time Steps Low-synchronization Arnoldi Algorithms with Application to Exponential Integrators
matrix flows	Two-dimensional fluids via matrix hydrodynamics
matrix hydrodynamics	Structure preservation in plasmas via matrix hydrodynamics
Matrix manifolds	Geometric low-rank approximation of the Zeitlin model of incompressible fluids on the sphere The Witten Laplacian on Riemannian Manifolds: Computational Methods for Saddle-Point Problems
Matrix pencil method	High-Precision Hilbert Transform from Discrete Uniform Samples: Extracting Non-Integer Algebraic Decay Orders via the Matrix Pencil Method
Maximal Monotone Operator	Iterative Solutions of Generalized Split Feasibility Problems
maximum flux path	StringNET: Neural Network based Variational Method for Transition Pathways
Maxwell's equation	Wave-number-explicit analysis for maxwell's equation with Dirichlet-to-Neumann truncation
Maxwell’s equations	Efficient Simulation of Surface Plasmon Polaritons on Complex Graphene Geometries
McKean-Vlasov equation	Convergence speed in distribution of finite particle systems to McKean-Vlasov-type equations using generators of measure-valued diffusions
McKean-Vlasov PDEs	A feedback-control perspective on sampling for Langevin and McKean-Vlasov dynamics
MCMC	AI and Molecular Dynamics: a theoretical perspective on why generative models can boost sampling Physics inspired Gaussian processes for Bayesian inverse problems Langevin Monte Carlo methods for Bayesian inference Numerical integrators for Langevin dynamics with boundary conditions MCMC on submanifolds: on and beyond constraints
MD	Uncertainty Quantification of Upscaling Thermal Transport
MDR	A Minimal-Deformation-Rate Framework for Surface Evolution: From Curvature Flows to Shape Optimization
mean curvature flow	Error estimates for a finite element method for anisotropic mean curvature flow Arbitrary-order structure-preserving discretizations for geometric curvature flows
Mean field games	Parallel-in-Time Preconditioning for Mean Field Games and Schroedinger Bridges
Mean--field interacting particle systems	Validity of the Norton formulation of non--equilibrium molecular dynamics for mean--field interacting particle systems
mean-field control	A quantitative limit theory for quadratic mean-field controls
mean-field dynamics	Convergence of the two-timescale gradient descent-ascent algorithm
mean-field equation	Agent-based models in Opinion Dynamics: model reduction and mean-field limits
mean-field limits	Coarse-Grained Modeling of Clustering Dynamics in Interacting Particle Systems
mean-field SDE	DeepSPoC: a deep learning based sequential propagation of chaos
Mean-field SDEs	Data-driven approximation of transfer operators for mean-field stochastic differential equations
mean-square dissipative	Bifurcations and uncertainty in mean square for SDEs
mean-square stability	Bifurcations and uncertainty in mean square for SDEs
Measure-valued diffusion	Convergence speed in distribution of finite particle systems to McKean-Vlasov-type equations using generators of measure-valued diffusions
measure-valued source term	Leak localisation with a measure source convection–diffusion model
mechanics	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates
Memory kernels	Memory Effects in Many-Body Open Quantum Systems: Transfer Tensors and Continuous Kernels
Mesh deformation / mesh quality	Arbitrary Lagrangian–Eulerian Schemes for Moving Interface Problems
Mesh-free method	Variational Gaussian approximation for the magnetic Schrödinger equation
Meshfree methods	Wavelet Galerkin Methods for the Helmholtz Equation and Elliptic Interface Problems
Metal-organic frameworks	Graph-Based Machine Learning Framework for Predicting Hydrogen Storage Capacity in Metal–Organic Frameworks
Metastability	Entropic metastability in the narrow escape problem Quasi-stationarity diagnostics with recurrent neural networks
Metric graphs	Bayesian Optimization on Networks
MHD	Helicity-preserving finite element schemes for magnetohydrodynamics
micropolar fluid	Spherically Symmetric Flow of a Compressible Real Micropolar Gas: Existence, Regularity, and Stabilization
Migrasome	How does Tspan4 shape migrasomes?
Mild Space Augmentation	An Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation
mimetic finite differences	Geometric Numerical Discretization of Fully Kinetic and Hybrid Drift-Kinetic Electromagnetic Quasineutral Models
Mimetic operators	The Parker Problem - An Update
min-max optimization	Convergence of the two-timescale gradient descent-ascent algorithm
minimal deformation rate	Arbitrary-order structure-preserving discretizations for geometric curvature flows
Minimal residual methods	Adaptive Minimal Residual Methods for Parabolic Problems on Locally Refined Space-Time Meshes
Minimum action method	An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials StringNET: Neural Network based Variational Method for Transition Pathways
minimum energy path	StringNET: Neural Network based Variational Method for Transition Pathways
MINRES	Multilevel Tau preconditioners for symmetrized multilevel Toeplitz systems with applications to solving space fractional diffusion equations
mixed FEM	A 3D-1D model of the electrostatic problem on the electrical treeing
mixed finite element method	Machine Learning Assisted Two-Level Mixed Finite Element Method for the Darcy--Forchheimer Model
mixed finite elements	Locking-free shells with structure-preserving mixed finite elements Stabilisation of the Navier⁠–Stokes equations by enstrophy preservation Structure-preserving Magnetic Relaxation in Stellarator Geometries
Mixed interpolation	A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity
mixed-dimensional model	A 3D-1D model of the electrostatic problem on the electrical treeing
Mixed-dimensional problems	A Localised Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems
mixing	Transport and mixing in fluid flows: a network-based approach
mixture approximation	Approximating distributions through greedy mixtures: an algorithmic framework.
modal regression	Kernel-based modal regression with right-censored data
Model Compression	Hardware aware dynamical low-rank training of large language models
Model Hierarchies	Model Hierarchies of Port-Hamiltonian Systems for Efficient Energy Network Simulation
Model order reduction	Combining dynamical low-rank approximation with local refinement strategies for proton radiation therapy One Step Forward, One Step Back: A Memory-Efficient Dynamical Low-Rank Scheme for the Adjoint State Method
Model reduction	Nemytskii neural operator: a nonlinear model reduction method for parametrized partial differential equations Agent-based models in Opinion Dynamics: model reduction and mean-field limits
Model selection	Weak-form PDE Identification with Optimal Test Functions Learned from Data
modeling	Extreme Scaling of a 1.5km global weather and climate model
Modified Helmholtz equation	Fast evaluation of layer and volume potentials for the modified Helmholtz equation
modulated Fourier expansion	Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations Analytical Approximation of Nonlinear Friedrichs Systems by Modulated Fourier Expansions
Molecular Dynamics	Accurate and robust analysis of molecular kinetics with random features Coarse-Grained Molecular Sampling with Machine Learning Velocity jumps for faster molecular dynamics simulations Preserving Transition Rates in Coarse-grained Models with Koopman Methods Efficient molecular dynamics simulations for confined systems: kernel approximations & random batch sampling Efficient computation of transport coefficients using the Green–Kubo formula with Girsanov’s reweighting Machine Learning for Coarse-Grained Molecular Sampling
Molecular simulation	Machine-learned coarse-graining for everything and everyone
Monge-Ampère equation	Inverse methods for optical design Convergence and error estimates for P_1 finite element method for the Monge-Ampère equation
Monotone Variational Inclusion Problem	Iterative Solutions of Generalized Split Feasibility Problems
Monte Carlo method	Multi-fidelity and multi-level Monte Carlo methods for kinetic models of traffic flow
Monte Carlo methods	Approximating distributions through greedy mixtures: an algorithmic framework.
Monte Carlo Sampling	An O(log N) Monte Carlo method for periodic Coulomb systems
Monte Carlo simulation	Adjoint Monte Carlo Simulation of Kinetic Equations with Reversible Random Number Generators
Morphology	Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamics
Moving boundary	Free boundary plasma equilibria with flexible coordinates
Moving contact line	Variational Modelling and Numerical Simulations for Evaporating Thin Droplets and Coffee-Ring Effect
moving contact lines	Contact Line Dynamics on Elastic Sheets
Moving Domain Problem	Higher Order Unfitted Space-Time Finite Element Methods
moving domains	Time-domain integral equations for the wave equation on moving domains
Moving interface	Dynamics of Hele-Shaw flow in Multi-connected Regions
Moving interface problems	Arbitrary Lagrangian–Eulerian Schemes for Moving Interface Problems
moving interfaces	Strong Stability of Cut Finite Element Methods for Parabolic Problems on Evolving Surfaces
multi-agent system	Boundary Consensus of Reaction-Diffusion Multi-Agent Systems under Restricted Observation
Multi-discriminator learning	Graph-informed GANs: Variational learning with Bayesian network structure
multi-fidelity methods	Multi-fidelity and multi-level Monte Carlo methods for kinetic models of traffic flow Multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties
Multi-interface	Dynamics of Hele-Shaw flow in Multi-connected Regions
Multi-Level Monte Carlo	Multi-Level Monte Carlo Training in Operator Learning Multi-fidelity and multi-level Monte Carlo methods for kinetic models of traffic flow
Multi-order fractional differential equations	Recent Advances in Spectrally Accurate Collocation Methods for Fractional Modelling
Multi-Resolution data	Multi-Level Monte Carlo Training in Operator Learning
Multi-time-step methods	Velocity jumps for faster molecular dynamics simulations
multigrade deep learning	Multigrade Neural Network Approximation and Layer-wise Geometric Rates
Multigrid	Efficient solvers for p-Laplace and related problems Machine Learning-Enhanced Multigrid for Convection-Dominated Flows
Multigrid methods	Iterative Solvers for Implicit Discretisations of the Boussinesq System via Patch-Wise Preconditioning
Multilevel	Sequential Monte Carlo for Bayesian Inference Using Randomized Likelihoods
multilevel Toeplitz matrices	Multilevel Tau preconditioners for symmetrized multilevel Toeplitz systems with applications to solving space fractional diffusion equations
Multimodal Prediction	Multimodal prediction of catheter ablation outcomes in patients with persistent atrial fibrillation
Multiphase fluid model	A fully-decoupled second-order-in-time and unconditionally energy stable scheme for the moving contact line problem
Multirate	Runge-Kutta methods for Nonlinearly Partitioned Equations Efficient Sensitivity Analysis for Systems with Multiple Time Scales or Fidelities
multirate infinitesimal methods	Multirate infinitesimal solutions of DAEs arising in power system simulations
Multirate integration	A Hierarchical Splitting Approach for N-Split Differential Equations
multirate methods	Accelerating Real-Time Boltzmann Transport Simulations with Adaptive Multirate Methods New Features and Applications in the SUNDIALS Library Second order explicit stabilized multirate method for stiff differential equations with error control
Multiscale	Treating different timescales in variational data assimilation for coupled systems A 3D-1D model of the electrostatic problem on the electrical treeing Atomistically-Informed Modelling of Dislocation Loops in Tungsten
Multiscale coupling	Multiscale Coupling of Random Deformation Flows for Accelerated Statistical Shape Modelling
Multiscale decomposition	A uniformly accurate multiscale time integrator for the nonlinear Klein–Gordon equation via simplified transmission conditions
multiscale hierarchical methods，	A Multiscale Hierarchical Segmentation Framework for Cell Fluorescence Microscopy
Multiscale Inference	Multiscale Inference of Cell Fate Dynamics and Gene Regulatory Networks Under Uncertainty
Multiscale methods	A Localised Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems
multiscale methpd	A Computational Multiscale Method for Heterogeneous Stokes Problems
multiscale simulation	Numerical Implementation of Fractional Differential Equations for Nonlinear Engineering Systems: Challenges and Considerations
Multisymplecticity	Finite element exterior calculus for time-dependent Hamiltonian partial differential equations
Multivariate Polynomial Regression	Tensor Networks for Machine Learning
Music Information Retrieval	Low-rank factorization for music audio signals analysis
N
narrow escape	Entropic metastability in the narrow escape problem
Natural Gradient	Efficient Derivative-Free Bayesian Inference for Large-Scale Inverse Problems
Navier--Stokes equations	An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
Navier-Stokes	Generalization Bounds for PINNs Solving the Navier-Stokes Equations
Navier-Stokes equations	An energy and entrophy-conserving enriched Galerkin method for incompressible Navier-Stokes equations
Navier–Stokes equations	Efficient and accurate spectral methods for PDEs in complex domains
Near-contact interactions	Accurate Near-Contact Simulation in 2D Stokes Flow via Two-Body Preconditioning
nested neural networks	Multigrade Neural Network Approximation and Layer-wise Geometric Rates
nested structures	Spherical Framelets from Spherical Designs
network evolution	On evolving network models and their influence on opinion formation and control
networks	Transport and mixing in fluid flows: a network-based approach Bayesian Optimization on Networks
Neumann boundary conditions	Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
Neural fields	An Isogeometric Collocation Framework for Neural Field Models on Multi-Patch NURBS Surfaces
neural flow	Neural Flow Networks and Operators: Abstract Frameworks and Universal Approximations
neural nets	Autodiff of Neural networks and application to DeepRitz and FEM
Neural network	A Deep Neural Network for Pricing American Options under Jump-Diffusion in High Dimension: A Backward Stochastic Differential Equation Approach
Neural network approximation	Mean-Field Molecular Dynamics Approximation of Quantum Statistical Observables with Machine Learning
neural network compression	A Nonlinear Tensor Network Architecture for Compressed End-to-End Learning
Neural network models	Low-Rank Residual Modeling for Error Correction in Time-Dependent PDE Simulations
Neural Network Potentials	Velocity jumps for faster molecular dynamics simulations
Neural Network Training	Frozen PINNs: Fast and Accurate Solutions of Time-Dependent PDEs Without Gradient-Descent
Neural network wavefunctions	Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
Neural Networks	Reversible numerical integrators for memory efficient deep learning Stability of Numerical Integrators on Riemannian Manifolds Neural network surrogates with uncertainty quantification for inverse problems in PDEs Neural Networks as a Discretization of Dynamical Systems Geometric Numerical Integration with Nonlinear Approximation Spaces Neural semi-Lagrangian method for high-dimensional advection-diffusion problems Geometric generalization of neural operators from kernel integral perspective Single-Neuron Optimization based Effective Training Method for Neural Networks with Smooth Activation Adaptive momentum and nonlinear damping for neural network training Low-rank training of tensor-structured neural networks Numerical Approximation of Ginzburg–Landau Energy Minimizers: Finite Elements and Neural Network Approaches Detecting unargmaxable outputs in low-rank classifiers Learning PDE solutions through Chebyshev encoding
Neural networks surrogates	Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations
neural ODE	Reversible numerical integrators for memory efficient deep learning
Neural ODEs	Stuart-Landau Oscillatory Graph Neural Network Constructive Conditional Normalizing Flows Neural Dynamical System with Algebraic Structure Constraint for Compact Geometric Learning
Neural operator	Nemytskii neural operator: a nonlinear model reduction method for parametrized partial differential equations Multi-Level Monte Carlo Training in Operator Learning Functional Data Analysis Using Neural Networks
Neural operator learning	Symplectic Spectral Neural Operators for Non-canonical Hamiltonian PDEs
Neural Operators	Symplectic Neural Operator for Learning Hamiltonian PDEs Physics-Informed Laplace Neural Operator: Data-Efficient and Out-of-Distribution Robust PDE Surrogate Modeling Learning Hamiltonian PDEs Neural Flow Networks and Operators: Abstract Frameworks and Universal Approximations FourCastNet 3: Geometric Neural Operators for Probabilistic Machine Learning Weather Forecast at Scale Physics-Informed Machine Learning Techniques with MATLAB
Neural PDE Solver	Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
Neural PDE solvers	Frozen PINNs: Fast and Accurate Solutions of Time-Dependent PDEs Without Gradient-Descent Learning Physics Directly From Corrupted Data.
Neural scaling laws	Input-state-output learning of port-Hamiltonian systems and neural scaling laws
Neural Simulators	Learning Physics Directly From Corrupted Data.
neuromorphic computing	Mental Math: Spiking Neuromorphic Circuits for Solving Partial Differential Equations
NFFT	Accelerated Machine Learning Atomic Energy and Force Predictions via Fast Kernel Summation
Nitsche's method	An arbitrary Lagrangian--Eulerian sliding interface method for fluid-structure interaction with a rotating rigid structure Modeling and simulation of fluid-structure-contact interaction A Penalty-free Asymmetric Nitsche's Method for Edge Elements
Non Linear Energy Sink	Analytical and Numerical Study of Nonlinear Energy Sinks with Odd-Power Stiffness and Damping Nonlinearities
Non-autonomous systems	Deep Predictor-Corrector Networks for Robust Parameter Estimation in Non-autonomous System with Discontinuous Inputs
Non-destructive Measurements	Thermal expectation estimation via controlled measurement Gibbs sampling
Non-equilibrium molecular dynamics	Validity of the Norton formulation of non--equilibrium molecular dynamics for mean--field interacting particle systems
Non-equilibrium systems	Constructing Macroscopic Dynamics using Deep Learning
non-Gaussian distributions	Marginal and conditional independence after diagonal transport
non-globally Lipschitz nonlinearity	Numerical approximations of stochastic time-fractional Burgers equations with fractional Gaussian noise
Non-linear eigenvalue problems	On the numerical analysis of mean-field models for electronic structure calculations in perfect crystals
Non-linear Fokker-Planck	Dynamical low-rank approximation of the non-linear Vlasov-Poisson-Fokker-Planck equation for weakly collisional plasmas
Non-local operators	High-Precision Hilbert Transform from Discrete Uniform Samples: Extracting Non-Integer Algebraic Decay Orders via the Matrix Pencil Method
Non-Markovian dynamics	Memory Effects in Many-Body Open Quantum Systems: Transfer Tensors and Continuous Kernels
Non-Parametric Statistics	Generalization Bounds for PINNs Solving the Navier-Stokes Equations
Non-smooth optimization	Deep Predictor-Corrector Networks for Robust Parameter Estimation in Non-autonomous System with Discontinuous Inputs
non-uniform FFT	Machine-Learning Interatomic Potentials for Long-Range Systems
nonequilibrium physics	Nonequilibrium polymer models for chromatin replication
Nonequilibrium Statistical Physics	AI and Molecular Dynamics: a theoretical perspective on why generative models can boost sampling
Nonlinear Approximation	Geometric Numerical Integration with Nonlinear Approximation Spaces
Nonlinear differential dynamics	Improving Carleman Linearization for Nonlinear Dynamics Simulation via Pivot Switching
Nonlinear differential equations	An end-to-end quantum algorithm for nonlinear fluid dynamics with bounded quantum advantage Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
nonlinear Dirac equation	An oscillation-rewinding splitting method for nonlinear Dirac equations with highly oscillatory solutions Time integration of highly-oscillatory, nonlinear Dirac equations
nonlinear dispersive equations	Low-regularity integrators for nonlinear dispersive equations via continuous formulations of numerical schemes
nonlinear dynamical systems	Uncertainty Quantification on Chemical Reactions Numerical Implementation of Fractional Differential Equations for Nonlinear Engineering Systems: Challenges and Considerations
Nonlinear dynamics	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
nonlinear elasticity	Numerical Analysis of Nonlinear Beam Networks
Nonlinear filtering	Positivity-Preserving Deep Density Filters for High-Dimensional SDEs
nonlinear Fokker-Planck equation	DeepSPoC: a deep learning based sequential propagation of chaos
nonlinear Friedrichs system	Analytical Approximation of Nonlinear Friedrichs Systems by Modulated Fourier Expansions
Nonlinear Klein-Gordon equation	Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations A uniformly accurate multiscale time integrator for the nonlinear Klein–Gordon equation via simplified transmission conditions
nonlinear parabolic partial differential equations	Parareal for parabolic equations with oscillatory coefficients
Nonlinear PDEs	TPDv algorithms for nonlinear PDEs with application to JKO schemes and interface dynamics
Nonlinear reaction-diffusion problems	Exponential Rosenbrock Methods without order reduction when integrating nonlinear initial boundary value problems
Nonlinear Schr\"{o}dinger equation	Second-order uniformly accurate method for the semiclassical nonlinear Schr\"odinger equation with initial data in $H^2$
Nonlinear Schrodinger equation	Time splitting for nonlinear Schrodinger equations: Strichartz estimates and consequences The nonlinear Schrodinger equation with rough potential: analysis and computations Explicit symmetric low-regularity integrators for the nonlinear Schrodinger equation A Wong–Zakai resonance-based integrator for the nonlinear Schrodinger equation with white noise dispersion
nonlinear Schroedinger equation	Computational methods for the nonlinear Schroedinger equation with low regularity potential and nonlinearity
nonlinear Schrödinger equation	Hybrid quantum-classical algorithms for complex nonlinear partial differential equations with Ginzburg-Landau potential and vortex motion laws Transverse instability studies for line solitary waves in cubic-quintic nonlinear Schrödinger equations Weighted finite difference methods for a nonlinear Schrödinger equation with highly oscillatory solutions in space and time
Nonlinear Schrödinger equations	Numerical study of biharmonic and polyharmonic nonlinear Schrödinger equations Structure-preserving low-regularity integrators for dispersive nonlinear equations Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation
Nonlinear tensor equations	Low-Rank Anderson Acceleration for Nonlinear Matrix and Tensor Equations
nonlinear wave equation	Time dependent acoustic scattering in full space from penetrable objects with nonlinearities
Nonlinear wave equations	Discontinuous Galerkin Methods for nonlinear wave equations via elliptic regularisation.
Nonlocal diffusion	A Fast Algorithm for the Fractional Fokker–Planck Equation in Arbitrary Dimensions Nonlocal Fisher-KPP Equation with Free Boundaries: Numerical Strategies for Accelerated Spreading and Sensitivity Analysis
Nonparametric Regression	Statistical Frameworks for Learning Nonlinear Mappings in Infinite Dimensions
nonrelativistic limit regime	Time integration of highly-oscillatory, nonlinear Dirac equations
Nonrelativistic regime	A uniformly accurate multiscale time integrator for the nonlinear Klein–Gordon equation via simplified transmission conditions
Nonstandard Finite Difference methods	Nonstandard Finite Difference and Modified Patankar Schemes
normalizing flow	DeepSPoC: a deep learning based sequential propagation of chaos
Normalizing flows	Constructive Conditional Normalizing Flows Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems
numerical algorithm and analysis	Sketch low-rank dynamics: orthogonal vs. oblique projections
numerical analysis	Hamiltonian Simulation with Magnus Expansion Kernel methods for differential equations: high-dimensional and physics-informed settings The nonlinear Schrodinger equation with rough potential: analysis and computations Convergence of finite elements for a bulk-surface coupled free boundary problem Graph zeta methods for efficient simulations of long-range interacting quantum lattices Building adjoint representations for tomography and compilation
numerical differential geometry	Two approaches to tensor fields on surfaces
Numerical Discretisation	Numerical methods for constraint Langevin dynamics with complex heat bath models
Numerical Homogenization	Quantum Enhanced Numerical Homogenization
Numerical integration	A comparative analysis of polynomial approximations and unitary splitting methods for the time-dependent Schrödinger equation
numerical integrators	Reversible numerical integrators for memory efficient deep learning The unconventional Hug integrator
numerical invariant measure	An explicit ergodicity-preserving fully discrete scheme for the stochastic Burgers--Huxley equation
Numerical methods	Numerical approximation for a stochastic Caputo fractional differential equation with multiplicative noise Shape and topology optimization for additive manufacturing processes Simulations of Contact-Line Dynamics Using a Novel Lattice-Boltzmann-Finite-Element Method Numerical Solution to 3D nonlinear differential equation (lid driven cavity)
numerical methods for ordinary differential equations	The random timestep Euler method and its continuous dynamics
Numerical methods for PDEs	An Entropy-Stable Discontinuous Spectral-Element Method for the Spherical Shallow Water Equation
Numerical methods for SPDEs	Strong Convergence of a Splitting Method for the Stochastic Complex Ginzburg-Landau Equation
numerical optimization	Swamp crossing methods for the canonical polyadic decomposition
numerical scheme	A Real Gas Spherically Symmetric Euler Framework with Self Gravity for Modelling Stellar Structure and Collapse
Numerical Simulations	Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos
Numerical Weather Prediction	An entropy stable well-balanced high order low Mach solver for atmospheric flows A numerical investigation of the Hopf bifurcation occurring in quasi-geostrophic channel flow
Numerics	Shape and topology optimization for additive manufacturing processes
NURBS surfaces	An Isogeometric Collocation Framework for Neural Field Models on Multi-Patch NURBS Surfaces
O
O(log N) Energy Evaluation	An O(log N) Monte Carlo method for periodic Coulomb systems
oblivious subspace embeddings	Sketch low-rank dynamics: orthogonal vs. oblique projections
observer design	Boundary Consensus of Reaction-Diffusion Multi-Agent Systems under Restricted Observation
Odd elasticity	Modelling disordered non-reciprocal active solids
ODEs	New Features and Applications in the SUNDIALS Library
Onsager's variational principle	A thermodynamically consistent domain embedding model for Cahn-Hilliard-Navier-Stokes equations with generalized Navier-slip boundary conditions
Onsager’s variational principle	Variational Modelling and Numerical Simulations for Evaporating Thin Droplets and Coffee-Ring Effect
Open quantum systems	Thermal expectation estimation via controlled measurement Gibbs sampling Memory Effects in Many-Body Open Quantum Systems: Transfer Tensors and Continuous Kernels Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
open-source	High-performance finite element simulations with MFEM
Operator learning	Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations Multi-Level Monte Carlo Training in Operator Learning Conformal Symplectic Neural Networks for Learning Multiple Energy-Dissipative Systems Statistical Frameworks for Learning Nonlinear Mappings in Infinite Dimensions Functional Data Analysis Using Neural Networks Laplacian Eigenfunction-Based Neural Operator for Learning Nonlinear Reaction–Diffusion Dynamics LSR-Net: Long-Short-Range Operator Learning for Pattern Dynamics on Manifolds
Operator theory	Accurate and robust analysis of molecular kinetics with random features
opinion dynamics	On evolving network models and their influence on opinion formation and control
Optimal control	Optimal control of an innovation diffusion model in Smartphone Markets Modeling and optimal control of SICA epidemic models On the variational formulation and discretization of optimal control problems for Lagrangian dynamics Trim turnpike property in discretized optimal control problems Analysis of a Phase Field Topology Optimization Problem with Cosserat Continuum and Thermal Dissipation
optimal error estimates	Computational methods for the nonlinear Schroedinger equation with low regularity potential and nonlinearity
Optimal overlap	On the optimal overlap in Optimized Schwarz Methods under computational cost constraint
Optimal Schwarz methods	On the optimal overlap in Optimized Schwarz Methods under computational cost constraint
optimal transport	Lipschitz-regularized gradient flows and generative particle algorithms Graph-informed GANs: Variational learning with Bayesian network structure Moving sample method for solving time-dependent partial differential equations Multiscale Inference of Cell Fate Dynamics and Gene Regulatory Networks Under Uncertainty
Optimal-complexity algorithms	A unified arbitrary-order Bernstein-Bézier discretization of H(div), H^1 and L^2 for 2D multi-physics problems
Optimality conditions	From fractional variational principles to classical optimization
optimisation	Smoothing and low-rank surrogates for non-smooth optimisation under uncertainty
Optimization	Hardware aware dynamical low-rank training of large language models Adaptive momentum and nonlinear damping for neural network training Fast Unsupervised Training of Deep Inverse Models Numerical Approximation of Ginzburg–Landau Energy Minimizers: Finite Elements and Neural Network Approaches Accelerating SAV-based optimisation via randomised low-rank Hessian approximation
optimization algorithms	Global optimization in very rugged landscapes for a kinetic beam heating problem
optimization landscape	Improved Global Landscape Guarantees for Low-rank Factorization in Synchronization
optimizers	Reducing Requirements on Data by Incorporating Structure
order conditions	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
order reduction	Order Reduction in Implicit-Explicit Runge-Kutta methods, and ways to overcome it
Ordinary differential equation	Computer-Assisted Search for Differential Equations Corresponding to Optimization Methods and Their Convergence Rates
Ordinary Differential Equations	Frozen PINNs: Fast and Accurate Solutions of Time-Dependent PDEs Without Gradient-Descent Explicit low-cost second derivative two-step peer methods Structure-Preserving Splitting Methods for Coupled Port-Hamiltonian Systems A Family of High Order Second Derivative Hybrid Block Methods for The Numerical Integration of Stiff Initial Value Problems in Ordinary Differential Equations
Organic Solar Cells	From Fabrication to Efficiency of Organic Photovoltaics: Modelling morphology and device performance
Ornstein Uhlenbeck Processes	Multiscale Inference of Cell Fate Dynamics and Gene Regulatory Networks Under Uncertainty
orthogonal polynomials	A sparse spectral method on domains bounded by planar algebraic curves
overdamped Langevin dynamics	Computational geometry of active matter: Space to insert hard spheres
Overdamped Langevin equation	Reentrance in a Hamiltonian flocking model
P
p-Laplacian	Efficient solvers for p-Laplace and related problems
parabolic optimal control	Parallel-in-Time algorithm for parabolic optimal control problems
Parabolic PDEs	Adaptive Minimal Residual Methods for Parabolic Problems on Locally Refined Space-Time Meshes
parabolic problems	Second order explicit stabilized multirate method for stiff differential equations with error control
parabolic surface PDEs	Strong Stability of Cut Finite Element Methods for Parabolic Problems on Evolving Surfaces
Parabolic-parabolic Keller-Segel (KS) system	SIPF-PIC: Efficient Large-Scale Simulation of 3D Chemotactic Systems
Parallel replica algorithm	Quasi-stationarity diagnostics with recurrent neural networks
parallel-in-time	Parallel-in-Time algorithm for parabolic optimal control problems
Parallel-in-time solver	Parallel-in-Time Preconditioning for Mean Field Games and Schroedinger Bridges
parameter efficient	Dynamical Low-Ranking Compression of Neural Networks with Robustness Under Adversarial Attacks
Parameter estimation	Deep Predictor-Corrector Networks for Robust Parameter Estimation in Non-autonomous System with Discontinuous Inputs
Parameter identification	Efficient State/Parameter Estimation via Dynamical Low-Rank Kalman Filters
parameterized partial differential equations	Nemytskii neural operator: a nonlinear model reduction method for parametrized partial differential equations
parametric FEM	A Minimal-Deformation-Rate Framework for Surface Evolution: From Curvature Flows to Shape Optimization
parametric finite element method	A Second-order Structure-preserving Parametric FEM for Surface Evolution Stable fully discrete parametric finite element methods for Willmore flow with applications
Parametric partial differential equations	Geometric generalization of neural operators from kernel integral perspective
parareal	Parareal for parabolic equations with oscillatory coefficients
Parker Problem	The Parker Problem - An Update
partial differential equation	Structure-preserving particle method for PDEs Numerical Solution to 3D nonlinear differential equation (lid driven cavity)
Partial differential equations	Frozen PINNs: Fast and Accurate Solutions of Time-Dependent PDEs Without Gradient-Descent Patterns and bifurcations in space-fractional reaction-diffusion models Firedrake: a differentiable programming framework for finite element simulation Fast evaluation of layer and volume potentials for the modified Helmholtz equation Physics-Informed Laplace Neural Operator: Data-Efficient and Out-of-Distribution Robust PDE Surrogate Modeling Enriching continuous Lagrange finite element approximation spaces using neural networks Discontinuous Galerkin Methods for nonlinear wave equations via elliptic regularisation. A Localised Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems Learning Image Derived PDE-Phenotypes from fMRI Data Finite element discretization of Yang–Mills connections
partial differential equations on manifolds	A Discontinuous Galerkin solver as an alternative dynamical core for the ICON model
Partial differential equations with singularities	Moving sample method for solving time-dependent partial differential equations
partially observed states	Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model
Partially observed stochastic control	A Pontryagin Maximum Principle on the Belief Space for Continuous-Time Stochastic Optimal Control with Discrete Observations
particle method	Energy-Dissipative and Conservative Discrete Gradient Particle Methods for Aggregation-Diffusion Equations and the Landau Equation DeepSPoC: a deep learning based sequential propagation of chaos An implicit geometric particle-in-cell method based on Galerkin difference for the Vlasov-Maxwell system Structure-preserving particle method for PDEs
Particle methods	Particle Methods for Plasma Equations Structure-preserving particle methods for collision operators in plasma physics
particle-based simulations	Transitions in proliferating active matter — particle-based simulations and effective models
Particle-in-cell (PIC)	SIPF-PIC: Efficient Large-Scale Simulation of 3D Chemotactic Systems
particle-in-cell methods	Geometric Numerical Discretization of Fully Kinetic and Hybrid Drift-Kinetic Electromagnetic Quasineutral Models
Partitioned explicit stabilized methods	Accelerating Global Gyrokinetic Simulations in GENE-X via Adaptive PIROCK Schemes
Partitioned multiphysics	Continuous and Time-discrete Error Bounds in the two norm for Waveform Relaxation for Heterogeneous Heat Equations
partitioned Runge-Kutta	Runge-Kutta methods for Nonlinearly Partitioned Equations
Patankar and Modified Patankar methods	Nonstandard Finite Difference and Modified Patankar Schemes
Patch preconditioning	Iterative Solvers for Implicit Discretisations of the Boussinesq System via Patch-Wise Preconditioning
path dependency	A quantitative limit theory for quadratic mean-field controls
Pattern discovery	Tensor Networks for Machine Learning
Pattern dynamics	LSR-Net: Long-Short-Range Operator Learning for Pattern Dynamics on Manifolds
pattern formation	Non mean field Vicsek type models for collective behaviour: Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
Patterns	Patterns and bifurcations in space-fractional reaction-diffusion models
PDE	Geometric PDE-based Neural Networks for Image Processing Simple and Efficient Discretization of Integral Operators on Deformed Spheres
PDE identification	Weak-form PDE Identification with Optimal Test Functions Learned from Data
PDE Learning	A Variational Framework for the Algorithmic Complexity of PDEs
PDE-based mesh motion	Arbitrary Lagrangian–Eulerian Schemes for Moving Interface Problems
PDE-constrained optimization	One Step Forward, One Step Back: A Memory-Efficient Dynamical Low-Rank Scheme for the Adjoint State Method Parallel-in-Time Preconditioning for Mean Field Games and Schroedinger Bridges
PDEs	Learning efficient solvers for time dependent PDEs on the sphere Simulations of Contact-Line Dynamics Using a Novel Lattice-Boltzmann-Finite-Element Method Learning Physics Directly From Corrupted Data.
Penning trap	Variational Gaussian approximation for the magnetic Schrödinger equation
Percolation	Modelling disordered non-reciprocal active solids
perturbo	Accelerating Real-Time Boltzmann Transport Simulations with Adaptive Multirate Methods
Phase field	Shape and topology optimization for additive manufacturing processes
phase retrieval	Conjugate Phase Retrieval on Graphs and with Applications to the Shift-Invariant Spaces
phase separation	Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models Transitions in proliferating active matter — particle-based simulations and effective models Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamics
phase transitions	Transitions in proliferating active matter — particle-based simulations and effective models
Phase-field	How does Tspan4 shape migrasomes?
phase-field models	Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models Analysis of a Phase Field Topology Optimization Problem with Cosserat Continuum and Thermal Dissipation
Phase-filed Modelling	A Thermodynamically Consistent Bulk-Surface PDE Model for Morphogen-Driven Receptor Dynamics and Lipid Raft Patterning
Phasefield modelling	From Fabrication to Efficiency of Organic Photovoltaics: Modelling morphology and device performance
Physics-guided Learning	Reliable Forecasting via Physics-Guided Stochastic Augmentation
Physics-Informed Deep Learning	Nonlinear Variational Integrators
Physics-informed Learning	Input-state-output learning of port-Hamiltonian systems and neural scaling laws Physics-Informed Laplace Neural Operator: Data-Efficient and Out-of-Distribution Robust PDE Surrogate Modeling
physics-informed machine learning	Physics-Informed Machine Learning Techniques with MATLAB Discovering Piecewise-Smooth Dynamics from Trajectory Data Rapid training of Hamiltonian Graph Networks using random features
Physics-informed neural network	A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
Physics-Informed Neural Networks	Moving sample method for solving time-dependent partial differential equations Frozen PINNs: Fast and Accurate Solutions of Time-Dependent PDEs Without Gradient-Descent Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models Enriching continuous Lagrange finite element approximation spaces using neural networks Accelerating SAV-based optimisation via randomised low-rank Hessian approximation Machine Learning Assisted Two-Level Mixed Finite Element Method for the Darcy--Forchheimer Model
Physics-inspired Neural Networks	Stuart-Landau Oscillatory Graph Neural Network
piecewise deterministic Markov processes	The random timestep Euler method and its continuous dynamics
piecewise regularity	Numerical issues in variable-order fractional differential equations with piecewise order transitions
piecewise-smooth dynamical systems	Discovering Piecewise-Smooth Dynamics from Trajectory Data
PINNs	Stability of the Second-order Elliptic Equation in Hölder Space and its Application to the PINN Method Physics-Informed Machine Learning Techniques with MATLAB Generalization Bounds for PINNs Solving the Navier-Stokes Equations Learning PDE solutions through Chebyshev encoding
PIROCK	Accelerating Global Gyrokinetic Simulations in GENE-X via Adaptive PIROCK Schemes
Pivot Switching	Improving Carleman Linearization for Nonlinear Dynamics Simulation via Pivot Switching
Plant–soil feedbacks	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
Plasma	Helicity-preserving finite element schemes for magnetohydrodynamics A IMEX-based spectral scheme with adaptive time-stepping for the Vlasov-Poisson system in the quasi-neutral limit
Plasma kinetic modeling	Energy Conserving Semi-Lagrangian Scheme for the Vlasov–Maxwell System
Plasma models	Particle Methods for Plasma Equations
plasma physics	Neural non-canonical Hamiltonian dynamics for long-time simulations Dynamical low-rank approximation of the non-linear Vlasov-Poisson-Fokker-Planck equation for weakly collisional plasmas One Step Forward, One Step Back: A Memory-Efficient Dynamical Low-Rank Scheme for the Adjoint State Method Structure-preserving particle methods for collision operators in plasma physics Free boundary plasma equilibria with flexible coordinates
plates	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates
Point clouds on manifolds	LSR-Net: Long-Short-Range Operator Learning for Pattern Dynamics on Manifolds
point-vortex dynamics	Numerical simulation of the Gross–Pitaevskii and magnetic Ginzburg-Landau equation via vortex tracking
Poisson geometry	Using Symplectic Realizations for the Simulation and Learning of Hamiltonian Dynamical Systems
Poisson integrators	Quadratic projectable Runge-Kutta methods
Polymer dynamics	Constructing Macroscopic Dynamics using Deep Learning
Polymer synthesis	A Reduced Model for Synthesis of Composite Polymer Particles
Polynomial approximations	A comparative analysis of polynomial approximations and unitary splitting methods for the time-dependent Schrödinger equation
polynomial dynamical systems	Integrable Splitting for Polynomial Dynamical Systems
polytopal method	A polytopal discrete de Rham scheme for Einstein's equations
Polytopes	Detecting unargmaxable outputs in low-rank classifiers
Pontryagin maximum principle	A Pontryagin maximum principle for optimal control problems involving generalized distributional-order derivatives
Pontryagin principle	A Pontryagin Maximum Principle on the Belief Space for Continuous-Time Stochastic Optimal Control with Discrete Observations
Population balance equations model Nondimensionalization	A Reduced Model for Synthesis of Composite Polymer Particles
poroelasticity	Decoupling Time Stepping Schemes for Poroelasticity
porous media	Machine Learning Assisted Two-Level Mixed Finite Element Method for the Darcy--Forchheimer Model
porous medium equation	Finite element scheme for the fractional porous medium equation with fractional pressure
Port-Hamiltonian systems	Input-state-output learning of port-Hamiltonian systems and neural scaling laws Structure-Preserving Splitting Methods for Coupled Port-Hamiltonian Systems Goal-Oriented Time Adaptivity For Linear pH-DAEs Of Index-1 Model Hierarchies of Port-Hamiltonian Systems for Efficient Energy Network Simulation
Positivity preservation	Nonstandard Finite Difference and Modified Patankar Schemes
positivity preserving schemes	Positivity-Preserving Finite Element Schemes for SPDEs
Positivity-Preserving	Positivity-Preserving Deep Density Filters for High-Dimensional SDEs
post-Lie algebra	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
post-quantum cryptography	Quantum Onion Routing
Preconditioned iterative method	Parallel-in-Time Preconditioning for Mean Field Games and Schroedinger Bridges
preconditioners	TPDv algorithms for nonlinear PDEs with application to JKO schemes and interface dynamics
Preconditioning	Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations Schrödingerization for quantum linear systems problems with near-optimal dependence on matrix queries Machine Learning-Enhanced Multigrid for Convection-Dominated Flows Accurate Near-Contact Simulation in 2D Stokes Flow via Two-Body Preconditioning Stage-segrated preconditioners for Galerkin time intergrators in Irksome Low-Rank Tensor Product Approximations for the Radiative Transfer Equation in Plane-Parallel Geometry Multilevel Tau preconditioners for symmetrized multilevel Toeplitz systems with applications to solving space fractional diffusion equations
pressure robustness	A Priori and a Posteriori Error Estimate for Pressure Robust Schemes for Incompressible Flow
Primal–dual algorithm	Parallel-in-Time Preconditioning for Mean Field Games and Schroedinger Bridges
probabilistic error analysis	Deterministic and probabilistic rounding error analysis of artificial neural networks in floating-point arithmetic
Probability and Density Estimation	Tensor Networks for Machine Learning
Probability flow ODE	Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
product-integration method	Numerical Implementation of Fractional Differential Equations for Nonlinear Engineering Systems: Challenges and Considerations
Production-destruction systems	Nonstandard Finite Difference and Modified Patankar Schemes
Progressive coarse-graining	Markovian Approximation for Nonlinear Overdamped Langevin Systems
Projected Inverse Iteration	Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
Projector splitting	Dynamical low-rank tensor train approximation for kinetic equations
Prolate Spheroidal Wave Functions	Accelerating Fast Ewald Summation with Prolates for Molecular Dynamics Simulations
proliferating active matter	Transitions in proliferating active matter — particle-based simulations and effective models
propagation of chaos	A quantitative limit theory for quadratic mean-field controls Validity of the Norton formulation of non--equilibrium molecular dynamics for mean--field interacting particle systems
Proper Orthogonal Decomposition	Low-Rank Residual Modeling for Error Correction in Time-Dependent PDE Simulations
Protein folding	Learning dynamical systems from data: Gradient-based dictionary optimization Accurate and robust analysis of molecular kinetics with random features
protein folding dynamics	Data-driven learning of transfer operators using randomized neural networks
Proton therapy	Combining dynamical low-rank approximation with local refinement strategies for proton radiation therapy
Pseudo-marginal	Sequential Monte Carlo for Bayesian Inference Using Randomized Likelihoods
pseudo-spectral methods	Extended Pseudo-spectral Physics-informed Neural Networks for Phase-field Models
Pseudodifferential calculus	Time splitting for nonlinear Schrodinger equations: Strichartz estimates and consequences
Pseudospectral methods	Non mean field Vicsek type models for collective behaviour:
PyTorch	Learning efficient solvers for time dependent PDEs on the sphere
Q
Quadrature	Fast evaluation of layer and volume potentials for the modified Helmholtz equation Simple and Efficient Discretization of Integral Operators on Deformed Spheres
quantitative convergence	Realisation of constraints in underdamped Langevin dynamics
quantities of interest	Goal-Oriented Low-Rank Tensor Decompositions for Numerical Simulation Data
Quantum	Building adjoint representations for tomography and compilation
Quantum algorithm	Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
Quantum algorithms	Nearly optimal quantum simulation of slow time-dependent Hamiltonians Quantum algorithms and lower bounds for differential equations Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
Quantum algorithms & computation	Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
Quantum algorithms for chemical calculations	Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
Quantum and HPC	Integrating Quantum Algorithms Into Classical Frameworks
Quantum canonical ensemble	Mean-Field Molecular Dynamics Approximation of Quantum Statistical Observables with Machine Learning
Quantum Carleman linearization	Improving Carleman Linearization for Nonlinear Dynamics Simulation via Pivot Switching
Quantum circuit	A Universal Dilation Method for Quantum Scientific Computing
Quantum complexity	Quantum algorithms for general nonlinear dynamics based on the Carleman embedding
quantum computing	Quantum Onion Routing A Universal Dilation Method for Quantum Scientific Computing Quantum Enhanced Numerical Homogenization Quantum Elastic Network Models and their Application to Graphene
Quantum Dynamics	Parallel Second-Order Time Integration of Low-Rank Tensors
quantum encryption	Quantum Onion Routing
Quantum error correction	Significantly more efficient Clifford+T synthesis for small-angle rotations and application to Trotterization
Quantum error mitigation	Significantly more efficient Clifford+T synthesis for small-angle rotations and application to Trotterization
Quantum for fluids	Integrating Quantum Algorithms Into Classical Frameworks
Quantum Gibbs Sampling	Thermal expectation estimation via controlled measurement Gibbs sampling
Quantum linear solvers	Integrating Quantum Algorithms Into Classical Frameworks
Quantum linear systems problem	Schrödingerization for quantum linear systems problems with near-optimal dependence on matrix queries
quantum networks	Quantum Onion Routing
Quantum simulation	Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
quantum spin systems	Graph zeta methods for efficient simulations of long-range interacting quantum lattices
Quantum turbulence	Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation
quasi Newton	mdBFGS: a Diagonal BFGS Method with Momentum for Stochastic Optimisation
Quasi optimal	Unified numerical analysis for thermoelastic diffusion and thermo-poroelasticity of thin plates
quasi-2D Confinement	Efficient molecular dynamics simulations for confined systems: kernel approximations & random batch sampling
Quasi-neutral	A IMEX-based spectral scheme with adaptive time-stepping for the Vlasov-Poisson system in the quasi-neutral limit
quasi-potential	An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
quasi-stationary distribution	Entropic metastability in the narrow escape problem Quasi-stationarity diagnostics with recurrent neural networks
Quasicrystals	Computing the spectrum of the Schrödinger equation with quasiperiodic potential
quasimode	Entropic metastability in the narrow escape problem
quasineutral models	Geometric Numerical Discretization of Fully Kinetic and Hybrid Drift-Kinetic Electromagnetic Quasineutral Models
Quasiperiodicity	Computing the spectrum of the Schrödinger equation with quasiperiodic potential
quenching phenomenon	Intercardinal Splitting Approximations for Kawarada Equations with Cross-Derivative Terms
R
Radiation transport	Combining dynamical low-rank approximation with local refinement strategies for proton radiation therapy
radiative transfer	Robust integrators in computational radiation therapy
radiative transfer equation	Low-Rank Tensor Product Approximations for the Radiative Transfer Equation in Plane-Parallel Geometry
Random Batch Sampling	Efficient molecular dynamics simulations for confined systems: kernel approximations & random batch sampling
Random differential equations	Multiscale Coupling of Random Deformation Flows for Accelerated Statistical Shape Modelling
random feature methods	Frozen PINNs: Fast and Accurate Solutions of Time-Dependent PDEs Without Gradient-Descent Rapid training of Hamiltonian Graph Networks using random features
Random Fourier feature representation	Mean-Field Molecular Dynamics Approximation of Quantum Statistical Observables with Machine Learning
random walks	Spectral clustering of temporal networks via spatio-temporal random walks
randomized neural networks	Data-driven learning of transfer operators using randomized neural networks
randomized numerical linear algebra	Sketch low-rank dynamics: orthogonal vs. oblique projections
Randomized Runge–Kutta methods	Error and Stability Analysis of a Randomized SDIRK Method
randomized sketching	Permutation-structured function estimation via tensor-train sketching
rank adaptive low-rank methods	Global optimization in very rugged landscapes for a kinetic beam heating problem
Rank-adapative	An Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation
Rare event	StringNET: Neural Network based Variational Method for Transition Pathways
Rare events	Importance sampling for Adaptive Multilevel Splitting
Rate-based analysis	Uncertainty Quantification on Chemical Reactions
rational approximation	Approximating the Matrix Exponential for Large Time Steps
Reaction kinetics	Uncertainty Quantification on Chemical Reactions
reaction-diffusion	Patterns and bifurcations in space-fractional reaction-diffusion models
Reaction-diffusion equation	A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
reaction-diffusion system	A Trace Finite Element Method for a Surface Reaction-Diffusion System Coupled with Surface Motion
reaction-diffusion systems	Boundary Consensus of Reaction-Diffusion Multi-Agent Systems under Restricted Observation
Reaction–diffusion systems	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points Discrete Analysis of Turing Instability for Splitting Methods
real gas	Spherically Symmetric Flow of a Compressible Real Micropolar Gas: Existence, Regularity, and Stabilization
real-time boltzmann transport equation	Accelerating Real-Time Boltzmann Transport Simulations with Adaptive Multirate Methods
reduced basis	Incremental Tensor-Train Reduced Basis Construction from Sequential Low-Rank Snapshots
Reduced dynamics	Low-Rank Residual Modeling for Error Correction in Time-Dependent PDE Simulations
reduced order modeling	Surrogate Modeling of 3D Rayleigh-Bénard Convection with Equivariant Autoencoders
Reduced Order Modelling (ROM)	Numerical Analysis of the Evolve-Filter-Relax Reduced Order Model for Buoyancy-Driven Flows
reduced-order modelling	From Koopman to polynomial embeddings for data-driven learning of nonlinear dynamics
Reduction Methods	Scientific Data Reduction Methods
Reduction of model complexity	A Reduced Model for Synthesis of Composite Polymer Particles
Reentrance phase behaviour	Reentrance in a Hamiltonian flocking model
Refinable vector functions	Multivariate vector subdivition schemes with a general matrix-valued filter
Reflected Riemannian gradient flow	A constrained saddle dynamics for computing electronic excited states
Regge finite element	Approximation of connection one-forms with finite elements
regularity	Spherically Symmetric Flow of a Compressible Real Micropolar Gas: Existence, Regularity, and Stabilization
regularity of Maxwell equations	hp-FEM for Maxwell’s equations in piecewise smooth media
Reissner-Mindlin	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates
relativistic Vlasov-Maxwell	Structure-preserving solutions of the relativistic moment equations
relaxation schemes	The limitations of magneto-frictional relaxation
relaxed micromorphic model	Intrinsic $H^{\mathrm{dev}}(\mathrm{Curl})$-conforming elements for planar relaxed micromorphic models
repeated cross-sectional	Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model
replication	Nonequilibrium polymer models for chromatin replication
reproducing kernel Hilbert space	Unbounded Density Ratio Estimation and Its Application to Covariate Shift Adaptation
Residual correction	Low-Rank Residual Modeling for Error Correction in Time-Dependent PDE Simulations
residual refinement	Multigrade Neural Network Approximation and Layer-wise Geometric Rates
Resolvent Operator	Iterative Solutions of Generalized Split Feasibility Problems
Resonance-based scheme	A Wong–Zakai resonance-based integrator for the nonlinear Schrodinger equation with white noise dispersion
resonances	Time integration of highly-oscillatory, nonlinear Dirac equations
Reversible diffusions	Stratonovich perturbation to improve the convergence to equilibrium
Richardson iteration	Low-Rank Tensor Product Approximations for the Radiative Transfer Equation in Plane-Parallel Geometry
Riemannian geometry	Mean-Square Convergence for SDEs on Riemannian Manifolds
Riemannian Langevin	Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
Riemannian manifold	A constrained saddle dynamics for computing electronic excited states
Riemannian manifolds	Stability of Numerical Integrators on Riemannian Manifolds Noise and stochastic processes on homogeneous spaces The Witten Laplacian on Riemannian Manifolds: Computational Methods for Saddle-Point Problems Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
Riemannian metric	Approximation of connection one-forms with finite elements
right-censored data	Kernel-based modal regression with right-censored data
risk measures	Smoothing and low-rank surrogates for non-smooth optimisation under uncertainty
RKHS	Fast and Accurate Tensor Decompositions on Infinite-Dimensional Function Spaces A kernel approach for the learning of Wasserstein geometric flows
robust time integration	Robust integrators in computational radiation therapy
Rosenbluth potentials	Dynamical low-rank approximation of the non-linear Vlasov-Poisson-Fokker-Planck equation for weakly collisional plasmas
rotating stratified flows	Centrifuged convection in an enclosed cube: boundary layer structures
Rotation matrices	A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity
rough potential	The nonlinear Schrodinger equation with rough potential: analysis and computations
rounding errors	Deterministic and probabilistic rounding error analysis of artificial neural networks in floating-point arithmetic
RTE	An Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation
Runge-Kutta	Efficient Sensitivity Analysis for Systems with Multiple Time Scales or Fidelities
Runge-Kutta method	Order Reduction in Implicit-Explicit Runge-Kutta methods, and ways to overcome it
Runge-Kutta methods	Doubling for Splitting Quadratic projectable Runge-Kutta methods Solving time fractional ODEs and PDEs.
Runge-Kutta-Chebyshev methods	Accelerating Global Gyrokinetic Simulations in GENE-X via Adaptive PIROCK Schemes
Runge–Kutta method	Variational Gaussian approximation for the magnetic Schrödinger equation
S
Saddle point	A constrained saddle dynamics for computing electronic excited states
Sample complexity	On Tackling High-Dimensional Nonconvex Optimization via Stochastic First-Order Methods
Sampling	Coarse-Grained Molecular Sampling with Machine Learning A feedback-control perspective on sampling for Langevin and McKean-Vlasov dynamics MCMC on submanifolds: on and beyond constraints A qualitative study of the reflected Kinetic Langevin process Machine Learning for Coarse-Grained Molecular Sampling Stratonovich perturbation to improve the convergence to equilibrium Adaptive Stepsizing for Stochastic Gradient Langevin Dynamics in Bayesian Neural Networks
sampling method	Langevin sampling methods with adaptive friction and stepsize
SAV	Accelerating SAV-based optimisation via randomised low-rank Hessian approximation
Scale spaces	Geometric PDE-based Neural Networks for Image Processing
scaling factor	An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
Scaling laws	Geometric regularisation of two-dimensional turbulence
Scaling transformation	A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
scaling-and-squaring	Computing Cholesky-factors of finite-horizon Gramians
Scarpi-type kernels	Subdiffusion Models with Evolving Memory Governed by Scarpi-Type Kernels
Schrodinger Equation	Numerical Investigation of the Schrödinger Equation with Low-Regularity Nonlinearity
Schrödinger	Global space-time low-complexity numerical methods for the time-dependent Schrödinger equation
Schrödinger equation	Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation Multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties Arbitrary high order splitting methods for linear Schrödinger equations with non-trivial compatibility conditions Geometric methods for electronic dynamics and excited-state calculations Computing the spectrum of the Schrödinger equation with quasiperiodic potential
Schrödingerization	Schrödingerization for quantum linear systems problems with near-optimal dependence on matrix queries
Scientific computing	A Universal Dilation Method for Quantum Scientific Computing Exploring Statistical and Numerical Designs for Generative Diffusions in Scientific Computing
scientific data analysis	Fast and Accurate Tensor Decompositions on Infinite-Dimensional Function Spaces
Scientific Machine Learning	Quasi-stationarity diagnostics with recurrent neural networks Single-Neuron Optimization based Effective Training Method for Neural Networks with Smooth Activation Geometric Property of the Brinkman Penalization Method for Hamiltonian PDEs and Its Applications A Variational Framework for the Algorithmic Complexity of PDEs Mental Math: Spiking Neuromorphic Circuits for Solving Partial Differential Equations Learning PDE solutions through Chebyshev encoding
scimal	Autodiff of Neural networks and application to DeepRitz and FEM
Score function	Wasserstein Bounds for generative diffusion models with Gaussian tail targets
SDE Modeling	Reliable Forecasting via Physics-Guided Stochastic Augmentation
SDIRK methods	Error and Stability Analysis of a Randomized SDIRK Method
Second derivatives	Explicit low-cost second derivative two-step peer methods
second order convergence	Second-order uniformly accurate method for the semiclassical nonlinear Schr\"odinger equation with initial data in $H^2$
second-order Langevin dynamics	Long-time behaviour of kinetic Langevin sampler
second-order optimality condition	Analysis of a Phase Field Topology Optimization Problem with Cosserat Continuum and Thermal Dissipation
sectorial problems	High order, variable step approximation of convolution equations
Seismic	Efficient Analysis of Geological Hypotheses using Bayesian Full Waveform Inversion
Seismic imaging	Enhancing Full Waveform Inversion and Least-Squares Reverse Time Migration via Learned and Regularized Source Wavelet Manipulation
Self-assembly	Modelling disordered non-reciprocal active solids
Self-organization	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
Self-similar solutions	Numerical study of dynamical regimes in the Landau–Lifshitz–Gilbert equation
Semi-implicit method	An implicit geometric particle-in-cell method based on Galerkin difference for the Vlasov-Maxwell system
semi-implicit semi-Lagrangian	Evaluating Global Scale Numerics on Small Scale Flows
semi-Lagrangian method	Semi-Lagrangian SAV method for the Vlasov-Maxwell equations Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
semi-Lagrangian scheme	Energy Conserving Semi-Lagrangian Scheme for the Vlasov–Maxwell System
semiclassical	Second-order uniformly accurate method for the semiclassical nonlinear Schr\"odinger equation with initial data in $H^2$
Semiclassical magnetic Schrödinger equation	Variational Gaussian approximation for the magnetic Schrödinger equation
semilinear parabolic problems	Exponential Runge–Kutta methods for parabolic equations with variable delay
Semilinear wave equation	Error analysis of splitting methods for 3D semilinear wave equations with finite-energy solutions
Sensitivity analysis	Efficient Sensitivity Analysis for Systems with Multiple Time Scales or Fidelities Geometric Adjoint Sensitivity Analysis and Hamiltonian Variational Integrators
Sequential Monte Carlo	Sequential Monte Carlo for Bayesian Inference Using Randomized Likelihoods
Serre-Green-Naghdi	Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
Shape and topology optimization	Shape and topology optimization for additive manufacturing processes
shape optimization	A Minimal-Deformation-Rate Framework for Surface Evolution: From Curvature Flows to Shape Optimization
shape reconstruction	A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems
shells	Locking-free shells with structure-preserving mixed finite elements
shift-invariant spaces	Conjugate Phase Retrieval on Graphs and with Applications to the Shift-Invariant Spaces
Shifted Boundary Method	Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
SI-DSA	An Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation
SICA model	Modeling and optimal control of SICA epidemic models
simulation data	Goal-Oriented Low-Rank Tensor Decompositions for Numerical Simulation Data
single-neuron optimization	Single-Neuron Optimization based Effective Training Method for Neural Networks with Smooth Activation
Singular kernels	Geometric generalization of neural operators from kernel integral perspective
singular perturbation theory	Geometric analysis of an epidemiological model for Olive Quick Decline Syndrome (OQDS)
singular solutions	Intercardinal Splitting Approximations for Kawarada Equations with Cross-Derivative Terms
Singularly Perturbed Problem	Error Analysis of Stabilized FEM for Singularly Perturbed Parabolic Delay-Differential Equations with Turning Point
Sketching	Convergence of flexible GMRES with and without randomized sketching
Slender body theory	Slender-body theory-like approaches for fibres by walls in slow viscous flow
sliding interface method	An arbitrary Lagrangian--Eulerian sliding interface method for fluid-structure interaction with a rotating rigid structure
Slow Invaraint Manifold	Analytical and Numerical Study of Nonlinear Energy Sinks with Odd-Power Stiffness and Damping Nonlinearities
Slow viscous flow	Slender-body theory-like approaches for fibres by walls in slow viscous flow
slow-fast dynamics	Geometric analysis of an epidemiological model for Olive Quick Decline Syndrome (OQDS)
small cut-cell problem	Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
Smartphone market adoption	Optimal control of an innovation diffusion model in Smartphone Markets
smoothing	Smoothing and low-rank surrogates for non-smooth optimisation under uncertainty
Sobolev approximation	Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
soft constraint limits	Realisation of constraints in underdamped Langevin dynamics
Software	New Features and Applications in the SUNDIALS Library
Software communities	The deal.II finite element library: What it is and how it delivers it
Software libraries	The deal.II finite element library: What it is and how it delivers it
solitary waves	Transverse instability studies for line solitary waves in cubic-quintic nonlinear Schrödinger equations
solitons	Numerical study of biharmonic and polyharmonic nonlinear Schrödinger equations
Solvability	Finite Volume Methods for Stokes Variational Inequalities
source-free systems	Integrable Splitting for Polynomial Dynamical Systems
space-fractional	Patterns and bifurcations in space-fractional reaction-diffusion models
Space-time	Space-time structure preserving discretisation for the wave equation
space-time discretization	Conservative space–time CutFEM for variable surface-tension two-phase flow
Space-time Methods	Nonlinear Variational Integrators
Space–time finite elements	Adaptive Minimal Residual Methods for Parabolic Problems on Locally Refined Space-Time Meshes
Sparse Bayesian learning	Data-driven Discovery of Asymmetric Interacting Particle Systems
sparse grids	Kernel interpolation in high dimensions with anisotropic sparse grids
Sparse regression	Weak-form PDE Identification with Optimal Test Functions Learned from Data
Sparse ridge regression	Learning Image Derived PDE-Phenotypes from fMRI Data
spatio-temporal oscillations	Analytical Approximation of Nonlinear Friedrichs Systems by Modulated Fourier Expansions
Spatiotemporal dynamics	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
SPDE	Agent-based models in Opinion Dynamics: model reduction and mean-field limits Positivity-Preserving Finite Element Schemes for SPDEs
Special Functions	Fractional Helmholtz equation
spectra	Finite element exterior calculus for spectra and pseudo-spectra of advection-diffusion of differential forms
spectral clustering	Learning graphons from data: Random walks, transfer operators, and spectral clustering Spectral clustering of temporal networks via spatio-temporal random walks
Spectral convergence	Towards spectral element solutions of full-potential Kohn-Sham equation
Spectral Galerkin approximations	On the numerical analysis of mean-field models for electronic structure calculations in perfect crystals
spectral gaps	Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
spectral method	Centrifuged convection in an enclosed cube: boundary layer structures
Spectral methods	Accurate Near-Contact Simulation in 2D Stokes Flow via Two-Body Preconditioning A sparse spectral method on domains bounded by planar algebraic curves Efficient and accurate spectral methods for PDEs in complex domains Computing the spectrum of the Schrödinger equation with quasiperiodic potential Numerical Solution to 3D nonlinear differential equation (lid driven cavity) Learning PDE solutions through Chebyshev encoding
spherical designs	Spherical Framelets from Spherical Designs
spherical framelets	Spherical Framelets from Spherical Designs
spherical symmetry	A Real Gas Spherically Symmetric Euler Framework with Self Gravity for Modelling Stellar Structure and Collapse Spherically Symmetric Flow of a Compressible Real Micropolar Gas: Existence, Regularity, and Stabilization
spiking neural networks	Mental Math: Spiking Neuromorphic Circuits for Solving Partial Differential Equations
Spline biorthogonal wavelets	Wavelet Galerkin Methods for the Helmholtz Equation and Elliptic Interface Problems
split-forms	Structure-Preserving Methods for the Compressible Euler Equations
Splitting and matrix-oriented techniques	Problem-oriented W-methods for advection-diffusion-reaction PDEs arising in vegetation dynamics
Splitting methods	Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling Intercardinal Splitting Approximations for Kawarada Equations with Cross-Derivative Terms An oscillation-rewinding splitting method for nonlinear Dirac equations with highly oscillatory solutions Doubling for Splitting Error analysis of splitting methods for 3D semilinear wave equations with finite-energy solutions Noise and stochastic processes on homogeneous spaces Splitting methods for momentum Langevin diffusions on Lie groups of compact type Arbitrary high order splitting methods for linear Schrödinger equations with non-trivial compatibility conditions Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation A Hierarchical Splitting Approach for N-Split Differential Equations Structure-Preserving Splitting Methods for Coupled Port-Hamiltonian Systems Convergence analysis for a full discretization of operator-valued differential Riccati equations Rigorous Error Analysis of Symmetric Zassenhaus Splittings in Infinite Dimensions Time integration of highly-oscillatory, nonlinear Dirac equations
Splitting scheme	Strong Convergence of a Splitting Method for the Stochastic Complex Ginzburg-Landau Equation
splitting schemes	Numerical integrators for Langevin dynamics with boundary conditions
stabilisation	Stabilisation of the Navier⁠–Stokes equations by enstrophy preservation A stabilised auxiliary variable approach and its higher order schemes for gradient flows
stability	Numerical study of biharmonic and polyharmonic nonlinear Schrödinger equations Stability of the Second-order Elliptic Equation in Hölder Space and its Application to the PINN Method Nonlocal Delay Problems Driven by the Caputo–Fabrizio Operator
stability analysis	Local Time Integration for Friedrichs’ Systems
stability and convergence	Numerical approximation for a stochastic Caputo fractional differential equation with multiplicative noise
Stability and quasi-optimality	Adaptive Minimal Residual Methods for Parabolic Problems on Locally Refined Space-Time Meshes
stabilization	Spherically Symmetric Flow of a Compressible Real Micropolar Gas: Existence, Regularity, and Stabilization
Stabilization Parameter	Error Analysis of Stabilized FEM for Singularly Perturbed Parabolic Delay-Differential Equations with Turning Point
stabilized finite element methods	Strong Stability of Cut Finite Element Methods for Parabolic Problems on Evolving Surfaces
stabilized second-order Runge–Kutta methods	Second order explicit stabilized multirate method for stiff differential equations with error control
State-space model	A filtering approach to quantifying discretisation errors in solving evolution equations
Statistical analysis	Accurate and robust analysis of molecular kinetics with random features
statistical geometry	Computational geometry of active matter: Space to insert hard spheres
Statistical Learning Theory	Towards the Theory of Physics-Informed Gaussian Processes Generalization Bounds for PINNs Solving the Navier-Stokes Equations
statistical physics	Stochastic processes with division, death and diffusion
Statistical shape modelling	Multiscale Coupling of Random Deformation Flows for Accelerated Statistical Shape Modelling
Statistics	Improved Global Landscape Guarantees for Low-rank Factorization in Synchronization
Steering dynamics	AI and Molecular Dynamics: a theoretical perspective on why generative models can boost sampling
Stefan problem	The two-phase Stefan problem on an evolving surface
stiff equations	Second order explicit stabilized multirate method for stiff differential equations with error control
stiff initial value problems	A Family of High Order Second Derivative Hybrid Block Methods for The Numerical Integration of Stiff Initial Value Problems in Ordinary Differential Equations
stiff order conditions	Order Reduction in Implicit-Explicit Runge-Kutta methods, and ways to overcome it
Stiff problems	Exploring directional split exponential integrators: from theory to efficient implementation Explicit stabilized implementation of singly diagonally implicit Runge-Kutta methods
stiffness	Order Reduction in Implicit-Explicit Runge-Kutta methods, and ways to overcome it
stiffness resilient methods	Stiffness resilient exponential integrators
stochastic algorithms	The random timestep Euler method and its continuous dynamics
stochastic bifurcation	Bifurcations and uncertainty in mean square for SDEs
stochastic Burgers equation	Numerical approximations of stochastic time-fractional Burgers equations with fractional Gaussian noise
stochastic Burgers--Huxley equation	An explicit ergodicity-preserving fully discrete scheme for the stochastic Burgers--Huxley equation
Stochastic Cahn--Hilliard equation	Ergodicity and invariant measure approximation of the stochastic Cahn–Hilliard equation via an explicit fully discrete scheme
Stochastic complex Ginzburg-Landau equation	Strong Convergence of a Splitting Method for the Stochastic Complex Ginzburg-Landau Equation
Stochastic delay differential equations	On splitting strategies for the numerical solution of stochastic delay differential equations with correlated noises
Stochastic delayed impulses	Event-triggered $\mu$-consensus control for nonlinear MASs with unknown-bound delays under stochastic delayed impulses
stochastic differential equation	Weak Generative Sampler
Stochastic differential equations	An exponential-free structure preserving integrator for stochastic Lie-Poisson systems Noise and stochastic processes on homogeneous spaces Splitting methods for momentum Langevin diffusions on Lie groups of compact type Mean-Square Convergence for SDEs on Riemannian Manifolds Dynamical Low-Rank Filters for Data Assimilation Post processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds A Magnus-based integrator for Brownian parametric semi-linear oscillators Multiscale Inference of Cell Fate Dynamics and Gene Regulatory Networks Under Uncertainty
Stochastic differential equations with Markovian switching	Tamed Milstein scheme for stochastic differential equations with Markovian switching with super-linear drift and diffusion coefficients
Stochastic dynamics	Nonequilibrium stochastic dynamics: Error estimates and variance reduction
Stochastic first-order methods	On Tackling High-Dimensional Nonconvex Optimization via Stochastic First-Order Methods
Stochastic Galerkin	Telescopic Projective Integration and Stochastic Galerkin for the Boltzmann Equation with Uncertainty
Stochastic gradient	Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling
Stochastic gradient MCMC	Adaptive Stepsizing for Stochastic Gradient Langevin Dynamics in Bayesian Neural Networks
stochastic gradients	Langevin Monte Carlo methods for Bayesian inference One Integrator Step Is Enough: Adaptive Ensemble Langevin Samplers
stochastic integral equations	Numerical approximation for a stochastic Caputo fractional differential equation with multiplicative noise
stochastic numerics	Mean-Square Convergence for SDEs on Riemannian Manifolds
stochastic optimisation	mdBFGS: a Diagonal BFGS Method with Momentum for Stochastic Optimisation
Stochastic oscillators	A Magnus-based integrator for Brownian parametric semi-linear oscillators
stochastic partial differential equations	Coarse-Grained Modeling of Clustering Dynamics in Interacting Particle Systems
stochastic PDEs	A discontinuous Galerkin method for the Dean-Kawasaki equation Numerical analysis of stochastic subdiffusion problems with fractional noise
Stochastic Processes	Stochastic processes with division, death and diffusion Generalization Bounds for PINNs Solving the Navier-Stokes Equations
Stochastic van der Pol oscillators	Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos
Stokes equations	Finite Volume Methods for Stokes Variational Inequalities
Stokes flow	Accurate Near-Contact Simulation in 2D Stokes Flow via Two-Body Preconditioning
Strang splitting	On splitting strategies for the numerical solution of stochastic delay differential equations with correlated noises
Streamline-Diffusion	Error Analysis of Stabilized FEM for Singularly Perturbed Parabolic Delay-Differential Equations with Turning Point
Strichartz estimates	Time splitting for nonlinear Schrodinger equations: Strichartz estimates and consequences
Strong convergence	On splitting strategies for the numerical solution of stochastic delay differential equations with correlated noises Tamed Milstein scheme for stochastic differential equations with Markovian switching with super-linear drift and diffusion coefficients
strong stability	Strong Stability of Cut Finite Element Methods for Parabolic Problems on Evolving Surfaces
Strongly Modulated Response	Analytical and Numerical Study of Nonlinear Energy Sinks with Odd-Power Stiffness and Damping Nonlinearities
structure preservation	Structure preservation and Deep Learning for Learning Mechanical Systems from Data Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables Energy-stable numerical methods for two-phase viscoelastic flows Reducing Requirements on Data by Incorporating Structure
Structure preserving	Neural non-canonical Hamiltonian dynamics for long-time simulations Space-time structure preserving discretisation for the wave equation An implicit geometric particle-in-cell method based on Galerkin difference for the Vlasov-Maxwell system Learning Hamiltonian PDEs
Structure Preserving Integrator	Nonlinear Variational Integrators
Structure preserving machine learning	Input-state-output learning of port-Hamiltonian systems and neural scaling laws
Structure preserving methods	Trim turnpike property in discretized optimal control problems
Structure preserving numerical method	Structure-preserving particle method for PDEs
Structure-Preservation	A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity Sparse identification of port-Hamiltonian systems from noisy data Structure-Preserving Splitting Methods for Coupled Port-Hamiltonian Systems Model Hierarchies of Port-Hamiltonian Systems for Efficient Energy Network Simulation
structure-preserving	Energy-Dissipative and Conservative Discrete Gradient Particle Methods for Aggregation-Diffusion Equations and the Landau Equation A Second-order Structure-preserving Parametric FEM for Surface Evolution Semi-Lagrangian SAV method for the Vlasov-Maxwell equations Finite element exterior calculus for time-dependent Hamiltonian partial differential equations Symplectic Spectral Neural Operators for Non-canonical Hamiltonian PDEs Structure-preserving particle methods for collision operators in plasma physics
Structure-preserving algorithms	Physics-consistent learning of circuit solutions using a topological decoupling of MNA An Entropy-Stable Discontinuous Spectral-Element Method for the Spherical Shallow Water Equation Finite element discretization of Yang–Mills connections
structure-preserving discretisation	Stabilisation of the Navier⁠–Stokes equations by enstrophy preservation
structure-preserving discretizations	Arbitrary-order structure-preserving discretizations for geometric curvature flows
structure-preserving finite elements	Numerical Analysis of Nonlinear Beam Networks
structure-preserving integrators	Structure-Preserving Integration for Magnetic Gaussian Wave Packet Dynamics
structure-preserving methods	Quadratic projectable Runge-Kutta methods Structure-Preserving Methods for the Compressible Euler Equations Geometric Numerical Discretization of Fully Kinetic and Hybrid Drift-Kinetic Electromagnetic Quasineutral Models
structure-preserving numerics	Structure-preserving solutions of the relativistic moment equations
structure-preserving scheme	Helicity-preserving finite element schemes for magnetohydrodynamics
structure-preserving splitting	Integrable Splitting for Polynomial Dynamical Systems
Subdiffusion with variable-order	Subdiffusion Models with Evolving Memory Governed by Scarpi-Type Kernels
Submanifolds	MCMC on submanifolds: on and beyond constraints
Subsurface	Efficient Analysis of Geological Hypotheses using Bayesian Full Waveform Inversion
Sum-of-Exponentials	LSR-Net: Long-Short-Range Operator Learning for Pattern Dynamics on Manifolds
Sum-of-Gaussians	Machine-Learning Interatomic Potentials for Long-Range Systems
sum-of-Gaussians approximation	Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation
summation by parts	Error analysis of splitting methods for 3D semilinear wave equations with finite-energy solutions
summation methods	Graph zeta methods for efficient simulations of long-range interacting quantum lattices
sundials	Accelerating Real-Time Boltzmann Transport Simulations with Adaptive Multirate Methods
Super intelligence	Necessary mechanisms for super AI and stopping hallucinations: The consistent reasoning paradox and the indeterminacy function
Super-linear coefficients	Tamed Milstein scheme for stochastic differential equations with Markovian switching with super-linear drift and diffusion coefficients
Superlinear error estimates	Continuous and Time-discrete Error Bounds in the two norm for Waveform Relaxation for Heterogeneous Heat Equations
surface diffusion	Arbitrary-order structure-preserving discretizations for geometric curvature flows
Surface evolution	A Second-order Structure-preserving Parametric FEM for Surface Evolution A Minimal-Deformation-Rate Framework for Surface Evolution: From Curvature Flows to Shape Optimization
Surface FEM	Error estimates for a finite element method for anisotropic mean curvature flow A Thermodynamically Consistent Bulk-Surface PDE Model for Morphogen-Driven Receptor Dynamics and Lipid Raft Patterning
surface Stokes flow	Two approaches to tensor fields on surfaces
Surrogate model	Smoothing and low-rank surrogates for non-smooth optimisation under uncertainty Towards the Theory of Physics-Informed Gaussian Processes
Surrogate modeling	Surrogate Modeling of 3D Rayleigh-Bénard Convection with Equivariant Autoencoders Geometric generalization of neural operators from kernel integral perspective
Surrogate modelling	Posterior Regression ImpOrtance Reweighting (PRIOR) Kernel interpolation in high dimensions with anisotropic sparse grids
surrogate models	Neural network surrogates with uncertainty quantification for inverse problems in PDEs
Sweep	An Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation
symmetric and explicit exponential wave integrator	Computational methods for the nonlinear Schroedinger equation with low regularity potential and nonlinearity
Symplectic	Finite element exterior calculus for time-dependent Hamiltonian partial differential equations
Symplectic geometry	Symplectic Neural Operator for Learning Hamiltonian PDEs Using Symplectic Realizations for the Simulation and Learning of Hamiltonian Dynamical Systems
Symplectic Integrators	Geometric Numerical Integration with Nonlinear Approximation Spaces Quadratic projectable Runge-Kutta methods
Symplectic methods	On the variational formulation and discretization of optimal control problems for Lagrangian dynamics On the relation of direct and indirect approaches for unconstrained optimal control problems
Symplectic splitting methods	Discrete Analysis of Turing Instability for Splitting Methods
Symplectic structure	Symplectic Spectral Neural Operators for Non-canonical Hamiltonian PDEs
symplectomorphism	Learning Hamiltonian PDEs
Synchronization	Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos Improved Global Landscape Guarantees for Low-rank Factorization in Synchronization
system identification	Input-state-output learning of port-Hamiltonian systems and neural scaling laws From Koopman to polynomial embeddings for data-driven learning of nonlinear dynamics Sparse identification of port-Hamiltonian systems from noisy data
T
Tamed Milstein scheme	Tamed Milstein scheme for stochastic differential equations with Markovian switching with super-linear drift and diffusion coefficients
tangential velocity	Stable fully discrete parametric finite element methods for Willmore flow with applications
Targted Energy Transfer	Analytical and Numerical Study of Nonlinear Energy Sinks with Odd-Power Stiffness and Damping Nonlinearities
Tau preconditioners	Multilevel Tau preconditioners for symmetrized multilevel Toeplitz systems with applications to solving space fractional diffusion equations
Taylor basis functions	A Curvilinear Lagrangian discontinuous Galerkin method for resistive magneto-hydrodynamics
Technology adoption dynamics	Optimal control of an innovation diffusion model in Smartphone Markets
Telescopic Projective Integration	Telescopic Projective Integration and Stochastic Galerkin for the Boltzmann Equation with Uncertainty
temporal networks	Spectral clustering of temporal networks via spatio-temporal random walks
tensor decompositions	Goal-Oriented Low-Rank Tensor Decompositions for Numerical Simulation Data Fast and Accurate Tensor Decompositions on Infinite-Dimensional Function Spaces
Tensor Factorization	Hardware aware dynamical low-rank training of large language models
Tensor network methods	Dynamics of two-dimensional dissipative quantum spin systems using tree tensor networks
Tensor Networks	Tensor Networks for Machine Learning Parallel Second-Order Time Integration of Low-Rank Tensors A Nonlinear Tensor Network Architecture for Compressed End-to-End Learning
tensor neural networks	Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation
Tensor product wavelets in Sobolev spaces	Wavelet Galerkin Methods for the Helmholtz Equation and Elliptic Interface Problems
tensor train	A tensor train numerical approach for Boltzmann equation Dynamical low-rank tensor train approximation for kinetic equations Permutation-structured function estimation via tensor-train sketching Cross Algorithms for Dynamical Matrix and Tensor Low-Rank Approximation in Fluid Mechanics Incremental Tensor-Train Reduced Basis Construction from Sequential Low-Rank Snapshots
tensor train decomposition	A Nonlinear Tensor Network Architecture for Compressed End-to-End Learning
Tensors	Low-rank training of tensor-structured neural networks
test-time adaptation	Fast Unsupervised Training of Deep Inverse Models
Tetrahedral spectral element method	Towards spectral element solutions of full-potential Kohn-Sham equation
theoretical analysis	The nonlinear Schrodinger equation with rough potential: analysis and computations
Thermal Expectation Estimation	Thermal expectation estimation via controlled measurement Gibbs sampling
thermal radiative transfer	A scalable hybrid low-rank scheme for thermal radiative transfer
Thermal Transport	Uncertainty Quantification of Upscaling Thermal Transport
Thermoelastic diffusion	Unified numerical analysis for thermoelastic diffusion and thermo-poroelasticity of thin plates
thin structures	An exact complex Reissner-Mindlin finite element formulation implemented via polytopal templates
Thin-film dynamics	Variational Modelling and Numerical Simulations for Evaporating Thin Droplets and Coffee-Ring Effect
Three-dimensional (3D) simulations	SIPF-PIC: Efficient Large-Scale Simulation of 3D Chemotactic Systems
time discretization	Neural Flow Networks and Operators: Abstract Frameworks and Universal Approximations
time integration	Runge-Kutta methods for Nonlinearly Partitioned Equations An oscillation-rewinding splitting method for nonlinear Dirac equations with highly oscillatory solutions Time integration of highly-oscillatory, nonlinear Dirac equations
Time splitting methods	Time splitting for nonlinear Schrodinger equations: Strichartz estimates and consequences
time stepping	Parareal for parabolic equations with oscillatory coefficients Stage-segrated preconditioners for Galerkin time intergrators in Irksome Decoupling Time Stepping Schemes for Poroelasticity
Time-dependent PDEs	Low-Rank Residual Modeling for Error Correction in Time-Dependent PDE Simulations
Time-dependent Schrödinger equation	A comparative analysis of polynomial approximations and unitary splitting methods for the time-dependent Schrödinger equation
Time-dependent variational approximation	Variational Gaussian approximation for the magnetic Schrödinger equation
Time-discrete analysis	Continuous and Time-discrete Error Bounds in the two norm for Waveform Relaxation for Heterogeneous Heat Equations
time-domain boundary integral equation	Time-domain integral equations for the wave equation on moving domains
time-domain boundary integral equations	Coupling Time‑Domain Boundary Integral Equations with Domain Methods or Nonlinear Boundary Dynamics
Time-fractional problems	Computationally Efficient Two-Grid ADI Scheme for Two-Dimensional Nonlinear Time-Fractional Reaction–Diffusion Equations
time-harmonic Maxwell equations	hp-FEM for Maxwell’s equations in piecewise smooth media
time-parallel time-integration	Parareal for parabolic equations with oscillatory coefficients
Time-Splitting Method	Transverse instability studies for line solitary waves in cubic-quintic nonlinear Schrödinger equations Numerical Investigation of the Schrödinger Equation with Low-Regularity Nonlinearity
Timestepping	Extended Krylov method for fully implicit Runge-Kutta methods
Toeplitz matrices	Multilevel Tau preconditioners for symmetrized multilevel Toeplitz systems with applications to solving space fractional diffusion equations
Topology optimization	Energy-stable inertial level-set flow for topology optimization
Topology preservation	A Topology Preserving, Energy Dissipative, High-order Lagrangian Finite Element Method for Magnetic Relaxation in Plasma
trace FEM	A Trace Finite Element Method for a Surface Reaction-Diffusion System Coupled with Surface Motion
Traffic flow	Multi-fidelity and multi-level Monte Carlo methods for kinetic models of traffic flow
training algorithm	Single-Neuron Optimization based Effective Training Method for Neural Networks with Smooth Activation
transfer operators	Learning graphons from data: Random walks, transfer operators, and spectral clustering Spectral clustering of temporal networks via spatio-temporal random walks Data-driven learning of transfer operators using randomized neural networks Data-driven approximation of transfer operators for mean-field stochastic differential equations Coarse-Grained Modeling of Clustering Dynamics in Interacting Particle Systems
Transfer tensors	Memory Effects in Many-Body Open Quantum Systems: Transfer Tensors and Continuous Kernels
Transformers	Adaptive momentum and nonlinear damping for neural network training
transition path computation	An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
transition paths	StringNET: Neural Network based Variational Method for Transition Pathways
Transmission conditions	A uniformly accurate multiscale time integrator for the nonlinear Klein–Gordon equation via simplified transmission conditions
transport	Transport and mixing in fluid flows: a network-based approach
Transport boundary condition	A Least-Squares Method for Non-Injective Gradient Mappings via the Mixed Monge-Ampère Equation
Transport coefficients	Validity of the Norton formulation of non--equilibrium molecular dynamics for mean--field interacting particle systems
Transport equations	Constructive Conditional Normalizing Flows
Traveling pulses	Traveling patterns and delayed feedbacks sustain ecosystems beyond classical tipping points
Traveling wave solution	A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
travelling wave solutions	Non mean field Vicsek type models for collective behaviour:
Tree tensor networks	Dynamics of two-dimensional dissipative quantum spin systems using tree tensor networks
trigonometric integrator	Error analysis of splitting methods for 3D semilinear wave equations with finite-energy solutions
Trotterization	Significantly more efficient Clifford+T synthesis for small-angle rotations and application to Trotterization
TSpan4	How does Tspan4 shape migrasomes?
Tucker	Cross Algorithms for Dynamical Matrix and Tensor Low-Rank Approximation in Fluid Mechanics
Tungsten	Atomistically-Informed Modelling of Dislocation Loops in Tungsten
Turbulence	Geometric regularisation of two-dimensional turbulence
Turbulence modelling	Geometric regularisation of two-dimensional turbulence
Turbulent Combustion	Cross Algorithms for Dynamical Matrix and Tensor Low-Rank Approximation in Fluid Mechanics
Turing instability	Discrete Analysis of Turing Instability for Splitting Methods
Turing patterns	Exploring directional split exponential integrators: from theory to efficient implementation
Turing's infallibility dilemma	Necessary mechanisms for super AI and stopping hallucinations: The consistent reasoning paradox and the indeterminacy function
Turning Point	Error Analysis of Stabilized FEM for Singularly Perturbed Parabolic Delay-Differential Equations with Turning Point
Turnpike property	Trim turnpike property in discretized optimal control problems
Two-derivative exponential Rosenbrock methods	Three New Classes of Exponential Integrators for Stiff and Highly Oscillatory Systems
Two-derivative exponential Runge-Kutta methods	Three New Classes of Exponential Integrators for Stiff and Highly Oscillatory Systems
Two-dimensional turbulence	Variational data assimilation in the latent space of an implicit-rank-minimising autoencoder
Two-grid approach	Computationally Efficient Two-Grid ADI Scheme for Two-Dimensional Nonlinear Time-Fractional Reaction–Diffusion Equations
two-level algorithm	Machine Learning Assisted Two-Level Mixed Finite Element Method for the Darcy--Forchheimer Model
two-phase flow	Energy-stable numerical methods for two-phase viscoelastic flows
two-phase incompressible flow	Conservative space–time CutFEM for variable surface-tension two-phase flow
Two-step peer methods	Explicit low-cost second derivative two-step peer methods
U
Unbounded delays	Event-triggered $\mu$-consensus control for nonlinear MASs with unknown-bound delays under stochastic delayed impulses
uncertainties	Multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties
Uncertainty	Efficient Analysis of Geological Hypotheses using Bayesian Full Waveform Inversion
Uncertainty Calibration	Information-Theoretic Learnable Conformal Prediction for Flexible Uncertainty Calibration in MLIPs
Uncertainty quantification	Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations Multi-fidelity and multi-level Monte Carlo methods for kinetic models of traffic flow Telescopic Projective Integration and Stochastic Galerkin for the Boltzmann Equation with Uncertainty Kernel methods for differential equations: high-dimensional and physics-informed settings Posterior Regression ImpOrtance Reweighting (PRIOR) A Dynamical Low-rank Multilevel Monte Carlo Estimator for High-Dimensional Kinetic Equations Smoothing and low-rank surrogates for non-smooth optimisation under uncertainty Generative AI for Uncertainty Quantification and Data Assimilation Data-driven Discovery of Asymmetric Interacting Particle Systems FourCastNet 3: Geometric Neural Operators for Probabilistic Machine Learning Weather Forecast at Scale Towards the Theory of Physics-Informed Gaussian Processes Uncertainty Quantification on Chemical Reactions
Unconditionally energy stable	A fully-decoupled second-order-in-time and unconditionally energy stable scheme for the moving contact line problem
Unconstrained optimal control	On the relation of direct and indirect approaches for unconstrained optimal control problems
unconventional superconductivity	Graph zeta methods for efficient simulations of long-range interacting quantum lattices
Underdamped Langevin Dynamics	Consistent Projection of Langevin Dynamics: Preserving Thermodynamics and Kinetics in Coarse-Grained Models Realisation of constraints in underdamped Langevin dynamics
Unfitted Finite Element Method	Higher Order Unfitted Space-Time Finite Element Methods
Unfitted finite element methods	Cut Finite Element Methods for Curvature‑Driven Interface Evolution Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
Unfitted mesh method	Modeling and simulation of fluid-structure-contact interaction
uniform-in-time convergence	An explicit ergodicity-preserving fully discrete scheme for the stochastic Burgers--Huxley equation
uniformly accurate	Second-order uniformly accurate method for the semiclassical nonlinear Schr\"odinger equation with initial data in $H^2$ Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations A uniformly accurate multiscale time integrator for the nonlinear Klein–Gordon equation via simplified transmission conditions
Unitary problems	Bounding the error of the truncated Magnus expansion for unitary problems
Unitary splitting methods	A comparative analysis of polynomial approximations and unitary splitting methods for the time-dependent Schrödinger equation
universal approximation	Neural Flow Networks and Operators: Abstract Frameworks and Universal Approximations Interpolation, approximation, and controllability of deep neural networks
Universal approximation property	A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
universal interpolation	Interpolation, approximation, and controllability of deep neural networks
unraveling scheme	Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations
Unsupervised learning	Fast Unsupervised Training of Deep Inverse Models
Unsupervised Machine Learning	Low-rank factorization for music audio signals analysis
Upscaling	Uncertainty Quantification of Upscaling Thermal Transport
UQ	Uncertainty Quantification of Upscaling Thermal Transport
V
Vakonomic discretization	Vakonomic Fluids
van der Waals pressure	A Real Gas Spherically Symmetric Euler Framework with Self Gravity for Modelling Stellar Structure and Collapse
Vapnik-Chervonenkis (VC) dimension	Approximation and Error Bounds for KANs: Applications to Dynamical System Discovery via Linear Multistep Methods
variable delay	Exponential Runge–Kutta methods for parabolic equations with variable delay
variable order	Numerical issues in variable-order fractional differential equations with piecewise order transitions
variable steps	High order, variable step approximation of convolution equations
variable stepsize	Langevin sampling methods with adaptive friction and stepsize
variable surface tension	Conservative space–time CutFEM for variable surface-tension two-phase flow
variable-order fractional system	A Fast BDF2 Convolution Quadrature for Reaction-Diffusion Equations with Time-Dependent Memory
Variance reduction	Nonequilibrium stochastic dynamics: Error estimates and variance reduction FeDLRT: Federated Dynamical Low-Rank Training
variational adaptivity	Energy-Based hp-Adaptivity for the Approximation of Ground States of the Gross–Pitaevskii Equation with Rotation
Variational crime	Approximation of connection one-forms with finite elements
Variational data assimilation	Treating different timescales in variational data assimilation for coupled systems
Variational Formulations	A Variational Framework for the Algorithmic Complexity of PDEs
Variational inequality	Finite Volume Methods for Stokes Variational Inequalities
Variational Inference	Efficient Derivative-Free Bayesian Inference for Large-Scale Inverse Problems Multiscale Coupling of Random Deformation Flows for Accelerated Statistical Shape Modelling
Variational Integrators	Geometric Numerical Integration with Nonlinear Approximation Spaces
Variational learning	Graph-informed GANs: Variational learning with Bayesian network structure
variational methods	On the variational formulation and discretization of optimal control problems for Lagrangian dynamics Numerical Analysis of Nonlinear Beam Networks
Variational Regularization	Inexact Algorithms for Bilevel Learning
Vector cascade algorithms	Multivariate vector subdivition schemes with a general matrix-valued filter
Vector subdivision schemes	Multivariate vector subdivition schemes with a general matrix-valued filter
Vegetation dynamics in semi-arid ecosystems	Problem-oriented W-methods for advection-diffusion-reaction PDEs arising in vegetation dynamics
Velocity jump processes	Velocity jumps for faster molecular dynamics simulations
vibrationally resolved electronic spectrum	Vibrationally resolved electronic spectra from Hagedorn wavepacket dynamics
Vicsek model	Non mean field Vicsek type models for collective behaviour:
Viscoelasticity	Energy-stable numerical methods for two-phase viscoelastic flows
Vlasov Maxwell	Particle Methods for Plasma Equations
Vlasov-Maxwell equation	Semi-Lagrangian SAV method for the Vlasov-Maxwell equations
Vlasov-Maxwell system	Energy Conserving Semi-Lagrangian Scheme for the Vlasov–Maxwell System An implicit geometric particle-in-cell method based on Galerkin difference for the Vlasov-Maxwell system
Vlasov-Poisson	A IMEX-based spectral scheme with adaptive time-stepping for the Vlasov-Poisson system in the quasi-neutral limit
Vlasov–Poisson equation	Scalability of high-dimensional Vlasov-Poisson simulations with communication-avoiding asynchronous discontinuous Galerkin
Volterra integral equations	Solving time fractional ODEs and PDEs.
Volume-preservation	Numerical preservation of measures of ODEs and SDEs with aromatic structures
Voronoi decomposition	Structure-preserving particle method for PDEs
vortex motion	Hybrid quantum-classical algorithms for complex nonlinear partial differential equations with Ginzburg-Landau potential and vortex motion laws
Vortex nucleation	Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation
vortex tracking	Numerical simulation of the Gross–Pitaevskii and magnetic Ginzburg-Landau equation via vortex tracking
W
Wasserstein distance	Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance One Integrator Step Is Enough: Adaptive Ensemble Langevin Samplers
Wasserstein flow	A kernel approach for the learning of Wasserstein geometric flows
Wasserstein gradient flows	A feedback-control perspective on sampling for Langevin and McKean-Vlasov dynamics
wave equation	Time-domain integral equations for the wave equation on moving domains A posteriori estimates and adaptive boundary elements for the wave equation
wave turbulence	From explicit formulas to Wave Kinetic theory for the Benjamin–Ono equation
wave-heat coupling	Finite element discretization of nonlinear models of ultrasound heating
wave-number-explicit analysis	Wave-number-explicit analysis for maxwell's equation with Dirichlet-to-Neumann truncation
wave-type problems	Local Time Integration for Friedrichs’ Systems
Waveform	Efficient Analysis of Geological Hypotheses using Bayesian Full Waveform Inversion
weak approximation	An explicit ergodicity-preserving fully discrete scheme for the stochastic Burgers--Huxley equation
Weak boundary conditions	A Penalty-free Asymmetric Nitsche's Method for Edge Elements
weak convergence	Numerical integrators for Langevin dynamics with boundary conditions
Weak initial singularity	Computationally Efficient Two-Grid ADI Scheme for Two-Dimensional Nonlinear Time-Fractional Reaction–Diffusion Equations
weather	Extreme Scaling of a 1.5km global weather and climate model
Weather forecasting	Learning efficient solvers for time dependent PDEs on the sphere
Weather Prediction	AI weather forecasting: Past, present and future FourCastNet 3: Geometric Neural Operators for Probabilistic Machine Learning Weather Forecast at Scale
well-balanced schemes	Structure-Preserving Methods for the Compressible Euler Equations
Well-Balancing	An entropy stable well-balanced high order low Mach solver for atmospheric flows
Westervelt's equation	Finite element discretization of nonlinear models of ultrasound heating
wetting dynamics	Contact Line Dynamics on Elastic Sheets
White noise dispersion	A Wong–Zakai resonance-based integrator for the nonlinear Schrodinger equation with white noise dispersion
Whittle-Matérn processes	Bayesian Optimization on Networks
Wiener algebra	Weighted finite difference methods for highly oscillatory nonlinear Klein–Gordon equations
Willmore flow	Stable fully discrete parametric finite element methods for Willmore flow with applications Error estimates for backward difference full discretization of Willmore flow for surfaces Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamics
Witten Laplacian	The Witten Laplacian on Riemannian Manifolds: Computational Methods for Saddle-Point Problems
Witten transform	Finite element antidynamo theorems and generalized Hodge theory
Wnt Signaling Dynamics	A Thermodynamically Consistent Bulk-Surface PDE Model for Morphogen-Driven Receptor Dynamics and Lipid Raft Patterning
Wong–Zakai approximation	A Wong–Zakai resonance-based integrator for the nonlinear Schrodinger equation with white noise dispersion
Z
Zakharov system	Exponential wave integrators for the Zakharov system
Zeitlin model	Geometric low-rank approximation of the Zeitlin model of incompressible fluids on the sphere
Zhidkov spaces	Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation