The field of matrix hydrodynamics dates back to the works of Vladimir Zeitlin, who used quantization theory to derive spatial discretization of the 2-D Euler equations. This approach gives a finite-dimensional, isospectral matrix flow that captures the rich geometric structure of the 2-D Euler equations. Recently, this approach to structure-preserving spatial discretization has been extended to several equations in fluid and plasma dynamics, such as the incompressible magnetohydrodynamic equations and the quasi-geostrophic equations. Moreover, the model and approach of Zeitlin in itself has deep connections to other areas of mathematics, such as representation theory and statistical mechanics. Our intention with this session is to bring together researchers within this field to present their most recent findings.

This minisymposium will highlight various numerical methods used in molecular dynamics to better approximate high dimensional averages with respect to Boltzmann-Gibbs probability measures, and sample dynamical quantities such as time-correlation functions or transition paths between two regions of the configuration space. Paradigmatic dynamics which are used to this end are Langevin dynamics (random perturbations of Hamiltonian dynamics) and their discretization. Efficient numerical methods can be devised by relying on various strategies such as probabilistic couplings and importance sampling, and/or through the use of techniques from control theory. This minisymposium will favor the emergence of a new generation of applied mathematicians on these topics (as all the speakers are PhD students or postdoctoral fellows), and more generally increase the visibility of molecular dynamics in Scicade conferences.

Dispersive partial differential equations (PDEs) play a fundamental role in many fields from science to engineering. There are various challenges in some practical problems such as rough data, high oscillations and random terms leading to loss of convergence and huge computational costs. From the perspective of computational mathematics, it is significant to design efficient numerical methods to solve these dispersive PDEs and provide an intuitive view for physical phenomena. The proposed minisymposium brings together experts of computational and applied mathematicians and computational scientists to provide an overview of current state-of-the-art and recent advances in the design and analysis of numerical methods for dispersive PDEs as well as their applications in various fields.

Many areas across computational science continue to face fundamental challenges posed by the curse of dimensionality with examples ranging from spin systems in quantum mechanics and computational radiation therapy to modern machine learning applications. These problems require representing and evolving extremely high-dimensional data, often rendering direct numerical simulation infeasible. In recent years, dynamical low-rank approximation has emerged as a powerful and versatile technique, enabling computations that were previously out of reach. This minisymposium brings together researchers from diverse application domains to present recent advances, share insights into current methodologies, and discuss both the analytical foundations and practical limitations of dynamical low-rank approaches. Beyond presenting recent analytical and methodological advances, the
minisymposium aims to identify unifying mathematical structures underlying dynamical low-rank methods, explore open challenges in
numerical analysis and algorithm design, and highlight emerging application areas. By fostering exchange between communities from
physics, engineering, and data science, we aim to enable new collaborations and chart future directions for this rapidly evolving field.

Numerical analysis for quantum mechanical models—ranging from the original Schrödinger equation to effective models such as density functional theory, post-Hartree–Fock methods, and the Gross–Pitaevskii equation—has not yet become very prominent within applied mathematics, despite the widespread use of quantum mechanical models across the sciences. Nevertheless, typical questions of numerical analysis, such as well-posedness, convergence, and scaling of the underlying methods, are actively being investigated. This mini-symposium will feature eight carefully selected talks on recent advances in this area. The emphasis will be on numerical analysis, with the aim of making the presentations accessible and engaging for the broader SciCADE community.

The study of interacting particle systems can be viewed as a multidisciplinary mathematical field with great progress continuing to be made and with new areas arising. This mini-symposium will focus on the study of agent-based models and their limiting behaviour for very large number of agents; this limiting behaviour is referred to as the mean-field limit of these systems. The discussion will not be limited to interacting agents (or particles) in a Euclidean space with all to all coupling, but will also include interacting particle systems on random graphs and networks. The aforementioned systems will be investigated from both the analytical perspective, i.e., via Fokker-Planck equations, analysis of SDEs and SPDEs, and the computational perspective, i.e., with the use of numerical methods, simulations, as well as data-driven methods. Additionally, some applications of these systems will be considered in the fields of opinion dynamics, epidemic spreading, active matter, and models for animal migration and movement.
This mini-symposium combines the fields of numerical methods, analysis of SDEs, SPDEs, PDEs, dynamical systems, computational statistics and optimization. Moreover the applications of interacting particle systems which will be discussed in this mini-symposium lie in the fields of computational biology, machine learning and molecular dynamics.

Scientific Machine Learning (SciML) has emerged as a transformative paradigm in computational science, bridging classical numerical analysis with modern data-driven methodologies. This mini-symposium aims to explore recent advances in neural solvers for differential equations, ranging from their theoretical foundations to cutting-edge applications in complex physical and engineering systems.
We will cover a broad spectrum of methodologies, with a particular focus on Physics-Informed Neural Networks (PINNs) and Neural Operators. The session seeks to address fundamental challenges in SciML, including the mathematical analysis of convergence and error bounds, optimization and training stability, scalability to high-dimensional or multiscale problems, and robustness in data-scarce or noisy settings.
This mini-symposium provides a platform for applied mathematicians, computer scientists, and engineers to exchange ideas, share recent breakthroughs, and foster collaborations that push the boundaries of how we solve and understand differential equations in the era of AI.

The primary focus of the mini-symposium is on geometric partial differential equations on surfaces and coupled bulk-surface systems, with an emphasis on rigorous numerical analysis and mesh-quality-preserving algorithms. Central themes are curvature-driven surface flows (mean curvature and Willmore-type bending flows, including surface diffusion), harmonic-map heat flows, and interface problems in which evolving geometry interacts with physical fields.

A unifying focus is the design and analysis of discretisations that respect intrinsic geometric or variational structure with provable convergence and a priori stability estimates. Attention will be paid to mesh-quality control via tangential-velocity or minimal-deformation principles, as well as to meshless and point-cloud approaches for complex, strongly deforming surfaces.

The programme will connect PDE theory, differential geometry and computational methods, and will highlight applications in cell biology and materials science. By bringing together experts on analysis, modelling and computation, the mini-symposium will foster exchange of ideas and stimulate new collaborations across these rapidly developing areas.

This mini-symposium brings together researchers at the intersection of numerical analysis, combinatorial algebra, and geometry to explore recent advances and emerging applications in the approximation of evolutionary ODEs and PDEs. Special emphasis will be placed on how recent algebraic results on tree-based structures, such as Butcher series, allow for the development of novel high-order, stable, and structure-preserving integrators for stiff, stochastic, and geometric dynamics. The aim is to foster interdisciplinary exchange between applied and pure mathematicians, highlighting the central role of algebraic and geometric techniques in modern geometric numerical integration.

Science has long been concerned with observing the world to see how it moves, and how to move it. Data-driven methods have been transformative for discovering dynamical systems that lie beyond the scope of traditional modelling. Conversely, ideas from dynamics and Numerical Analysis lie at the core of many emerging AI techniques. This minisymposium explores this growing synergy. We bring together keywords such as the inverse problem view of dynamics discovery, data-driven model order reduction, structure preserving numerical integration, and differential equations on graphs.

SciCADE has long served as a premier forum for advances in the numerical analysis and scientific computing of differential equations. In this context, the rapid emergence of learning-based approaches for solving partial differential equations (PDEs) raises important questions that are central to the SciCADE community: convergence, stability, computational complexity, and efficiency.

This minisymposium focuses on the mathematical foundations and algorithmic design of learning-based PDE solvers, including neural operators, physics-informed neural networks, and hybrid surrogate models. While these methods have shown strong empirical performance, their rigorous analysis remains an active area of research. The session will highlight recent progress on convergence guarantees, approximation and complexity bounds, variational and operator-theoretic formulations, and structure-preserving learning strategies.

A particular emphasis is placed on energy-based and gradient-flow formulations, which naturally connect learning-based solvers with classical numerical analysis and provide tools for understanding stability, scalability, and energy efficiency. By situating learning-based PDE solvers within established SciCADE themes, this minisymposium aims to foster dialogue between researchers in numerical analysis, scientific computing, and machine learning, and to identify principled pathways toward reliable, interpretable, and efficient computational methods for PDEs.

Magnetohydrodynamics (MHD) studies the dynamics of electrically conducting fluids, such as plasmas, under the influence of magnetic fields. MHD plays a crucial role in many critical scientific and engineering problems of today, such as in solar physics (e.g., the mechanism of coronal heating and space weather forecast), astrophysics (e.g., behaviours of stellar magnetic fields and jets from black holes), and renewable energy (the design of controllable fusion devices such as stellarators). Numerical computation is indispensable in these areas. Despite decades of efforts, reliable and efficient numerical computation for MHD systems is still a challenge, and often prevents substantial progress in the field. In particular, the MHD system has rich geometric and topological structures, which translate to crucial physical mechanisms. Failure to preserve such structures in numerics may lead to the failure of numerical simulations (which can often be difficult to detect due to the lack of visible indications). Progress in structurepreserving finite element methods sheds light on some long-standing challenges in computational MHD, and yet new challenges arise. The proposed minisymposium aims to bring together researchers working on solar physics, fusion energy, and structure-preserving numerical methods to communicate and foster interdisciplinary and international collaborations.

Handling complex and evolving geometries remains a central challenge in the numerical solution of PDEs, particularly in applications ranging from multiphase flows to cardiac dynamics. While classical approaches rely on explicit, body-fitted meshes, these can be computationally demanding for large topological changes or moving interfaces.

Over the last two decades, implicit and unfitted discretisation methods have emerged as a robust alternative. By combining a fixed background mesh with an implicit domain description—such as a Level-set or Phase-field function—these methods circumvent the bottlenecks of traditional mesh generation.

This minisymposium brings together researchers to present recent advances in this field, aiming to facilitate discussions on current challenges and future research directions. The sessions will cover a spectrum of keywords including Finite Element and Boundary Integral Methods. Contributions will range from high-performance implementation to rigorous mathematical analysis of static and moving domain problems.

This minisymposium will highlight various numerical methods used in molecular dynamics to better approximate high dimensional averages with respect to Boltzmann-Gibbs probability measures, and sample dynamical quantities such as time-correlation functions or transition paths between two regions of the configuration space. Paradigmatic dynamics which are used to this end are Langevin dynamics (random perturbations of Hamiltonian dynamics) and their discretization. Efficient numerical methods can be devised by relying on various strategies such as probabilistic couplings and importance sampling, and/or through the use of techniques from control theory. This minisymposium will favor the emergence of a new generation of applied mathematicians on these topics (as all the speakers are PhD students or postdoctoral fellows), and more generally increase the visibility of molecular dynamics in Scicade conferences.

Dispersive partial differential equations (PDEs) play a fundamental role in many fields from science to engineering. There are various challenges in some practical problems such as rough data, high oscillations and random terms leading to loss of convergence and huge computational costs. From the perspective of computational mathematics, it is significant to design efficient numerical methods to solve these dispersive PDEs and provide an intuitive view for physical phenomena. The proposed minisymposium brings together experts of computational and applied mathematicians and computational scientists to provide an overview of current state-of-the-art and recent advances in the design and analysis of numerical methods for dispersive PDEs as well as their applications in various fields.

Many areas across computational science continue to face fundamental challenges posed by the curse of dimensionality with examples ranging from spin systems in quantum mechanics and computational radiation therapy to modern machine learning applications. These problems require representing and evolving extremely high-dimensional data, often rendering direct numerical simulation infeasible. In recent years, dynamical low-rank approximation has emerged as a powerful and versatile technique, enabling computations that were previously out of reach. This minisymposium brings together researchers from diverse application domains to present recent advances, share insights into current methodologies, and discuss both the analytical foundations and practical limitations of dynamical low-rank approaches. Beyond presenting recent analytical and methodological advances, the
minisymposium aims to identify unifying mathematical structures underlying dynamical low-rank methods, explore open challenges in
numerical analysis and algorithm design, and highlight emerging application areas. By fostering exchange between communities from
physics, engineering, and data science, we aim to enable new collaborations and chart future directions for this rapidly evolving field.

Numerical analysis for quantum mechanical models—ranging from the original Schrödinger equation to effective models such as density functional theory, post-Hartree–Fock methods, and the Gross–Pitaevskii equation—has not yet become very prominent within applied mathematics, despite the widespread use of quantum mechanical models across the sciences. Nevertheless, typical questions of numerical analysis, such as well-posedness, convergence, and scaling of the underlying methods, are actively being investigated. This mini-symposium will feature eight carefully selected talks on recent advances in this area. The emphasis will be on numerical analysis, with the aim of making the presentations accessible and engaging for the broader SciCADE community.

Scientific Machine Learning (SciML) has emerged as a transformative paradigm in computational science, bridging classical numerical analysis with modern data-driven methodologies. This mini-symposium aims to explore recent advances in neural solvers for differential equations, ranging from their theoretical foundations to cutting-edge applications in complex physical and engineering systems.
We will cover a broad spectrum of methodologies, with a particular focus on Physics-Informed Neural Networks (PINNs) and Neural Operators. The session seeks to address fundamental challenges in SciML, including the mathematical analysis of convergence and error bounds, optimization and training stability, scalability to high-dimensional or multiscale problems, and robustness in data-scarce or noisy settings.
This mini-symposium provides a platform for applied mathematicians, computer scientists, and engineers to exchange ideas, share recent breakthroughs, and foster collaborations that push the boundaries of how we solve and understand differential equations in the era of AI.

Kinetic equations model physical phenomena that can be described as an ensemble of particles moving in a position-velocity phase space, subject to collision events. Simulating such models is typically computationally expensive due to the high dimensionality of the phase space. Hence, a wide range of dedicated numerical schemes has been developed in recent decades to perform efficient simulations. In addition to numerical challenges, practical problems involving such models are often affected by uncertainty due to either unknown environmental factors or physics. Mathematically, this can take the form of, e.g, uncertain model parameters or initial conditions. In this minisymposium, we gather researchers working on quantifying uncertainty for kinetic models, both in the forward sense (propagating uncertainties through simulations) and inverse sense (estimating unknown quantities given known data or simulation results).

Machine learning and data driven approaches have become active research areas within numerical analysis, following the increasing demand of solving high-dimensional, complex, and large scale computational problems. This minisymposium aims to bring together active researchers on the interface of numerical analysis and machine learning theory to exchange new ideas, methodologies, and theories. In the minisymposium, we will discuss research keywords including stochastic gradient methods for optimization, and data driven approaches for the solution of differential equations. By fostering the interaction between numerical analysis and machine learning theory, the minisymposium will discuss emerging challenges, share new insights, and push forward the research of principled, efficient, and reliable data driven methods for numerical analysis.

This mini-symposium brings together researchers at the intersection of numerical analysis, combinatorial algebra, and geometry to explore recent advances and emerging applications in the approximation of evolutionary ODEs and PDEs. Special emphasis will be placed on how recent algebraic results on tree-based structures, such as Butcher series, allow for the development of novel high-order, stable, and structure-preserving integrators for stiff, stochastic, and geometric dynamics. The aim is to foster interdisciplinary exchange between applied and pure mathematicians, highlighting the central role of algebraic and geometric techniques in modern geometric numerical integration.

Stochastic differential equations on manifolds arise naturally in problems where randomness evolves under geometric constraints. In such settings, classical Euclidean numerical methods, such as the Euler-Maruyama method, generally fail to respect the geometry of the underlying space and may therefore produce large errors. This motivates the development of novel approximation methods that remain on the manifold and converge to the true solution of the SDE. Such stochastic dynamics arise in applications including molecular dynamics, rigid-body dynamics, robotics, and stochastic sampling methods in statistics and machine learning. This minisymposium will bring together recent advances in the analysis, approximation and implementation of numerical methods for manifold-valued SDEs.

SciCADE has long served as a premier forum for advances in the numerical analysis and scientific computing of differential equations. In this context, the rapid emergence of learning-based approaches for solving partial differential equations (PDEs) raises important questions that are central to the SciCADE community: convergence, stability, computational complexity, and efficiency.

This minisymposium focuses on the mathematical foundations and algorithmic design of learning-based PDE solvers, including neural operators, physics-informed neural networks, and hybrid surrogate models. While these methods have shown strong empirical performance, their rigorous analysis remains an active area of research. The session will highlight recent progress on convergence guarantees, approximation and complexity bounds, variational and operator-theoretic formulations, and structure-preserving learning strategies.

A particular emphasis is placed on energy-based and gradient-flow formulations, which naturally connect learning-based solvers with classical numerical analysis and provide tools for understanding stability, scalability, and energy efficiency. By situating learning-based PDE solvers within established SciCADE themes, this minisymposium aims to foster dialogue between researchers in numerical analysis, scientific computing, and machine learning, and to identify principled pathways toward reliable, interpretable, and efficient computational methods for PDEs.

Magnetohydrodynamics (MHD) studies the dynamics of electrically conducting fluids, such as plasmas, under the influence of magnetic fields. MHD plays a crucial role in many critical scientific and engineering problems of today, such as in solar physics (e.g., the mechanism of coronal heating and space weather forecast), astrophysics (e.g., behaviours of stellar magnetic fields and jets from black holes), and renewable energy (the design of controllable fusion devices such as stellarators). Numerical computation is indispensable in these areas. Despite decades of efforts, reliable and efficient numerical computation for MHD systems is still a challenge, and often prevents substantial progress in the field. In particular, the MHD system has rich geometric and topological structures, which translate to crucial physical mechanisms. Failure to preserve such structures in numerics may lead to the failure of numerical simulations (which can often be difficult to detect due to the lack of visible indications). Progress in structurepreserving finite element methods sheds light on some long-standing challenges in computational MHD, and yet new challenges arise. The proposed minisymposium aims to bring together researchers working on solar physics, fusion energy, and structure-preserving numerical methods to communicate and foster interdisciplinary and international collaborations.

Dynamical systems and deep learning are two seemingly separate fields. However, it has been observed that they have many connections, from designing new neural network architectures from discretizations of dynamical systems to new solution approaches for dynamical systems. This area has seen a large amount of progress with key areas being structure preservation, robustness guarantees and interpretability of neural networks. The minisymposium will discuss new advancements in the area both from a theoretical as well as an application perspective.

Complex networks are a powerful tool for analyzing a wide range of real-world systems, from social and biological interactions to physical and technological infrastructures. Understanding the structure of such networks is essential for uncovering the fundamental mechanisms that drive system behavior. For instance, detecting clusters can reveal meaningful functional or organizational subunits, while identifying hubs helps identify influential or important elements within the system. In many applications, real-world systems often evolve in time, giving rise to: (1) dynamics on networks, such as epidemic spreading, synchronization, or opinion formation; and (2) dynamics of networks, where the network topology changes due to e.g. adaptive rewiring. These two perspectives naturally connect network science and dynamical systems theory that enables a deeper understanding of how network structure shapes temporal behavior and vice versa. In this mini-symposium, we aim to bring together researchers from dynamical systems, network science and scientific computing to explore recent advances in model reduction, transfer operator approaches and spectral clustering, with particular focus on dynamical networks and random processes on networks.

Inspired by the growing interaction between the deterministic and stochastic communities for the design of efficient integrators with geometric and multiscale features, the goal of this minisymposium is to bring together leading researchers working on such key aspects of time integration methods for deterministic and stochastic dynamics. This includes in particular multiscale slow-fast problems, highly oscillatory problems and geometric problems for which the preservation of key invariants and geometric structures reveals essential for an accurate and reliable approximation, in particular in high or even infinite dimension.

We aim to bring researchers together who are working on approximation of SDEs from different aspects, for example particle approximation of McKean Vlasov SDEs, numerics for SPDEs, numerics for SDEs on manifolds, and application of SDEs and their approximations in sampling and optimization.

Dispersive partial differential equations (PDEs) are crucial in numerous applications. Efficient numerical methods and rigorous analysis are essential for reliable solutions and for understanding the underlying physical phenomena. This mini-symposium will focus on recent advances in numerical methods and applications related to dispersive PDEs, including keywords such as rough solutions, conservation properties, long-time behavior, and oscillatory solutions.

Molecular dynamics (MD) simulation has become one of the most popular tools for computational studies of properties in nano/micro scale systems across various areas. However, the trade-off between accuracy and efficiency remains a major challenge in the community. Density functional theory (DFT)-level MD is accurate but expensive and limited in terms of time and system size, while classical MD is fast but falls short in capturing quantum effects such as long-range charge transfer. To overcome these issues, innovative mathematical, computational, and modeling techniques are necessary. These techniques range from methods in numerical analysis to advanced tools in stochastic algorithms and machine learning. A successful combination of these techniques requires a platform for discussion among experts from different fields including chemistry, physics, and various branches of applied mathematics. This mini-symposium aims to provide the first steps toward such a platform by bringing together analysts, mathematical physicists, theoretical chemists, and computational physicists.

In this minisymposium, we present recent developments in the field of 'Computational quantum dynamics and semiclassical analysis' -- two areas at the intersection of mathematics, chemistry, physics, and scientific computing that have seen remarkable progress in recent years. A key equation of quantum dynamics is the time-dependent Schrödinger equation. For this fundamental differential equation, the major challenge is the curse of dimensionality, as the dimension of the configuration space of the underlying Hilbert space or the dimension of the Hilbert space itself grows exponentially with the number of sites/particles. In addition, the solutions are typically highly oscillatory. Model order reduction techniques and mesh-free methods, that exploit closeness to classical mechanics, have proved to be very promising in overcoming these issues. This includes low-rank tensor methods to dynamically evolve the Schrödinger equation in a low dimensional manifold and mesh-free Gaussian wave packets where the wave function is approximated by a small number of multidimensional Gaussians. In addition, developments in high-performance computing enable the large-scale simulations required in modern applications.

The minisymposium aims to make the keyword accessible to a broad audience at SciCADE by focusing on the numerical analysis aspects and bringing together researchers from different fields.

Numerical simulations of kinetic equations are now routinely used to study important phenomena e.g. in plasma physics or rarefied gas flow. However, the up to six-dimensional phase space makes such simulations extremely expensive. In addition, adding collisions can further exacerbate this problem and introduces significant stiffness. In this mini-symposium, we will consider recent advances in dealing with these problems in both particle methods and grid-based methods. The talks in the mini-symposium span from modern complexity reduction to integrating collision operators into particle schemes while preserving physical structure.

Recently, the mathematical foundations of deep learning from a continuous perspective have attracted increasing attention. This mini-symposium aims to draw connections from dynamical systems, differential equations, control theory, and the mathematical theory of deep learning. The goal is to establish a rigorous theoretical framework to better understand—and provide guidance for—the design and training of deep neural networks, with a particular focus on approximation, optimization, generalization, and stability properties.

Many areas of applied mathematics, including nuclear fusion, radiation therapy or quantum mechanics, involve solving high-dimensional, time-dependent problems. Despite rapid advances in computing power, obtaining solutions with sufficiently fine resolution often remains infeasible.

Dynamical low-rank approximation (DLRA) has quickly emerged as a powerful numerical method for tackling such high-dimensional, time-dependent PDEs. In DLRA, the solution evolves on a low-rank manifold by restricting the dynamics to its tangent space. Recent progress in higher-order, structure-preserving, parallelizable, and rank-adaptive matrix and tensor integrators has further enabled accurate simulation of complex high-dimensional systems.

Nevertheless, applying DLRA to real-world problems presents significant challenges. These range from mathematical issues, such as incorporating boundary conditions and adaptive meshes, to software and hardware considerations, including scalability on HPC systems and parallelization across CPUs and GPUs. This minisymposium brings together researchers from both applications and methodology to discuss the current challenges and state of the art.

Physical scenarios in reality often involve different scales. This includes the time scale, space scale and many other physical parameters of different size. This brings multiple scales to the governing equations, and mathematically the limits of the scaling parameters can be categorized into Hilbert’s six problem. The multiscale scales in the models usually make the solutions highly oscillatory in time and/or space. The widely considered examples include the semi-classical limit regime of nonlinear Schrodinger equation, dispersionless limit regime of KdV equation, non-relativistic limit of nonlinear Klein-Gordon equations, and Vlasov equations with strong-magnetic field. The temporal and spatial oscillations make traditional numerical methods less efficient, brining strong restrictions to mesh size for stability and accuracy. To overcome this issue, many multiscale methods have been proposed in past decades, and they are still under developing for more efficiency, higher order accuracy and structure preservation.
This minisymposium aims to bring together researchers that are active on developing multiscale methods and analysis for highly oscillatory problems, and share their recent works and ideas.

Machine learning (ML) and inverse problems (IP) are two rapidly evolving research fields that, although historically distinct, have become increasingly intertwined. The mathematical framework of inverse problems—centered on ill-posedness, regularization, and stability analysis—provides a solid theoretical foundation for understanding, interpreting, and improving modern learning algorithms. Meanwhile, machine learning offers powerful data-driven tools that can enhance or even replace traditional model-based approaches in solving complex inverse problems where analytical formulations are difficult or incomplete.

This minisymposium aims to bring together researchers working at the intersection of these domains to exchange new ideas, methodologies, and applications. It will highlight recent progress in combining theoretical and data-driven perspectives, including operator learning and hybrid model–data frameworks. Contributions will span both linear and nonlinear settings, addressing applications from medical imaging, fluid dynamics, and environmental science.

The proposed minisymposium will feature contributions spanning a wide range of keywords—from fundamental mathematical insights to emerging applications in medical imaging, fluid dynamics, environmental science and beyond—reflecting the vitality and diversity of current research. Hosting this session at SciCADE, a premier forum for advances in scientific computing and differential equations, provides an ideal platform to connect experts in inverse problems, machine learning, artificial intelligence, and computational science. By fostering dialogue across numerical analysis, optimization, and data science, the minisymposium aims to catalyse new collaborations and showcase how mathematical rigor and data-centric innovation together advance the frontiers of modern applied mathematics.

Quantum computing is emerging as a potentially transformative paradigm for scientific computing, with rapidly developing algorithms for linear systems, eigenvalue problems, optimisation, and the simulation of both Hamiltonian and non-Hamiltonian dynamics. At the same time, many questions remain open regarding structure-preserving, complexity, error analysis, and the practical relevance of these algorithms for concrete models arising in differential equations and applied analysis.
This minisymposium brings together researchers working at the interface of quantum algorithms, numerical analysis, and applications in physics and engineering. The talks will cover theoretical and methodological foundations of quantum algorithms, including algorithmic frameworks, complexity guarantees, stability and error analysis, and implementation-oriented perspectives.
Alongside methodological developments, the minisymposium will include illustrative applications that reflect the breadth of quantum scientific computing, such as quantum algorithms for lattice field theories and lattice gauge theories, and sampling-based quantum approaches to machine learning (including quantum annealing perspectives). The goal is to foster cross-disciplinary exchange, clarify the current state of the art, and identify problem classes with clear mathematical structure and practical relevance where quantum advantage may be achievable.

This minisymposium aims to bring together international experts in structure-preserving algorithms to exchange insights on recent advances in the theory, development, and applications in simulating complex physical systems with geometric properties—such as symplecticity, conservation of energy, momentum, and invariants, or dissipation laws etc.

While classical numerical methods provide precision, stability, and strong theoretical guarantees, they can be computationally demanding and require problem-specific expertise. Recent advances in artificial intelligence (AI) have introduced data-driven, general-purpose models capable of efficient, flexible, and real-time scientific simulations. At the same time, many fundamental properties of AI models—such as stability, robustness, precision, and numerical reliability—remain less well understood than those of traditional algorithms.
This minisymposium highlights the growing role of AI as a transformative tool for scientific computing, while emphasizing the crucial contributions of numerical analysis in understanding and strengthening AI-based methods. Topics will include the use of AI to address challenges in numerical PDEs and scientific simulation, as well as the application of linear algebra, geometric analysis, and rounding error analysis to characterize and mitigate vulnerabilities in AI models

Inspired by the growing interaction between the deterministic and stochastic communities for the design of efficient integrators with geometric and multiscale features, the goal of this minisymposium is to bring together leading researchers working on such key aspects of time integration methods for deterministic and stochastic dynamics. This includes in particular multiscale slow-fast problems, highly oscillatory problems and geometric problems for which the preservation of key invariants and geometric structures reveals essential for an accurate and reliable approximation, in particular in high or even infinite dimension.

We aim to bring researchers together who are working on approximation of SDEs from different aspects, for example particle approximation of McKean Vlasov SDEs, numerics for SPDEs, numerics for SDEs on manifolds, and application of SDEs and their approximations in sampling and optimization.

Dispersive partial differential equations (PDEs) are crucial in numerous applications. Efficient numerical methods and rigorous analysis are essential for reliable solutions and for understanding the underlying physical phenomena. This mini-symposium will focus on recent advances in numerical methods and applications related to dispersive PDEs, including keywords such as rough solutions, conservation properties, long-time behavior, and oscillatory solutions.

Molecular dynamics (MD) simulation has become one of the most popular tools for computational studies of properties in nano/micro scale systems across various areas. However, the trade-off between accuracy and efficiency remains a major challenge in the community. Density functional theory (DFT)-level MD is accurate but expensive and limited in terms of time and system size, while classical MD is fast but falls short in capturing quantum effects such as long-range charge transfer. To overcome these issues, innovative mathematical, computational, and modeling techniques are necessary. These techniques range from methods in numerical analysis to advanced tools in stochastic algorithms and machine learning. A successful combination of these techniques requires a platform for discussion among experts from different fields including chemistry, physics, and various branches of applied mathematics. This mini-symposium aims to provide the first steps toward such a platform by bringing together analysts, mathematical physicists, theoretical chemists, and computational physicists.

The analysis and use of computational methods for time-dependent boundary integral equations have matured significantly in recent years. Various approaches and research communities are continually advancing state-of-the-art algorithms to produce efficient and reliable methods for these equations. The minisymposium aims to connect these communities, including researchers working on schemes based on the convolution quadrature method, the space-time Galerkin method, and asymptotic expansions in the context of time-domain scattering.

Scientific machine learning has emerged as a powerful paradigm for integrating data-driven models with scientific knowledge encoded in differential equations. This mini-symposium focuses on recent advances in modern optimization techniques that enable efficient and reliable training of scientific learning models. In particular, we explore optimization strategies for problems arising from scientific computing and machine learning.

The session highlights challenges unique to scientific learning, including stiff dynamics, high-dimensional parameter spaces, and the need to preserve physical structure. Contributions will present new algorithms and theoretical insights that improve convergence, stability, and scalability of optimization methods in these settings. Topics of interest include gradient-based and adjoint methods, structure-preserving optimization, implicit differentiation, and large-scale training techniques for models governed by differential equations, and stochastic methods. By bringing together researchers from numerical analysis, optimization, and scientific machine learning, this mini-symposium aims to foster discussion on how modern optimization tools can accelerate progress in computational science and engineering.

Many areas of applied mathematics, including nuclear fusion, radiation therapy or quantum mechanics, involve solving high-dimensional, time-dependent problems. Despite rapid advances in computing power, obtaining solutions with sufficiently fine resolution often remains infeasible.

Dynamical low-rank approximation (DLRA) has quickly emerged as a powerful numerical method for tackling such high-dimensional, time-dependent PDEs. In DLRA, the solution evolves on a low-rank manifold by restricting the dynamics to its tangent space. Recent progress in higher-order, structure-preserving, parallelizable, and rank-adaptive matrix and tensor integrators has further enabled accurate simulation of complex high-dimensional systems.

Nevertheless, applying DLRA to real-world problems presents significant challenges. These range from mathematical issues, such as incorporating boundary conditions and adaptive meshes, to software and hardware considerations, including scalability on HPC systems and parallelization across CPUs and GPUs. This minisymposium brings together researchers from both applications and methodology to discuss the current challenges and state of the art.

Physical scenarios in reality often involve different scales. This includes the time scale, space scale and many other physical parameters of different size. This brings multiple scales to the governing equations, and mathematically the limits of the scaling parameters can be categorized into Hilbert’s six problem. The multiscale scales in the models usually make the solutions highly oscillatory in time and/or space. The widely considered examples include the semi-classical limit regime of nonlinear Schrodinger equation, dispersionless limit regime of KdV equation, non-relativistic limit of nonlinear Klein-Gordon equations, and Vlasov equations with strong-magnetic field. The temporal and spatial oscillations make traditional numerical methods less efficient, brining strong restrictions to mesh size for stability and accuracy. To overcome this issue, many multiscale methods have been proposed in past decades, and they are still under developing for more efficiency, higher order accuracy and structure preservation.
This minisymposium aims to bring together researchers that are active on developing multiscale methods and analysis for highly oscillatory problems, and share their recent works and ideas.

The proposed minisymposium will highlight recent advances in wavelets and framelets, numerical analysis for partial differential equations (PDEs), and numerical integration for high-dimensional data — these areas that are increasingly interconnected in modern scientific computing. Wavelets and framelets provide powerful multiscale representations that have transformed approximation theory, signal processing, and numerical algorithms. Their ability to capture localized features makes them particularly effective for solving PDEs with complex geometries, irregular data, or multiscale phenomena. Numerical analysis for PDEs remains a cornerstone of computational science, with ongoing developments in stability, adaptivity, and efficiency driving progress in applications. Numerical integrations such as spherical designs play a fundamental role in high-dimensional data analysis and applications. This minisymposium is designed to unite researchers working at the intersection of harmonic analysis, numerical PDEs, and high-dimensional data analysis. By bringing together experts in wavelets/framelets, PDE discretization, and analysis, we aim to highlight the synergies between theoretical and numerical approaches to scientific computing. Our vision is to foster collaboration across these communities, showcase cutting-edge advances, and inspire new methodologies that address the challenges of multiscale modeling, scientific computing, high-dimensional analysis, and their applications.

There has been a wide interest in data-driven learning of dynamical systems, e.g., identifying the governing equations for a system of ordinary differential equations (ODEs), learning the associated transfer operators and their spectral decompositions that help us analyze the global behavior of the system, and approximation of solutions to partial differential equations (PDEs), which is an important problem in computational science and engineering. A lot of research has been done in developing data-driven techniques that help us in accomplishing the above tasks, e.g., extended dynamic mode decomposition (EDMD), sparse identification of nonlinear dynamics (SINDy), a number of neural network (NN)-based techniques, etc. There are, however, still many challenges and bottlenecks in these methods. For example, using NN as an ansatz for the solution of PDEs has proven a challenge in terms of training time and approximation accuracy. With active research in addressing these challenges, in this minisymposium, we aim at bringing together researchers working on several aspects of this rich, interdisciplinary field, including theory, modeling, algorithm development, and applications.

Quantum computing is emerging as a potentially transformative paradigm for scientific computing, with rapidly developing algorithms for linear systems, eigenvalue problems, optimisation, and the simulation of both Hamiltonian and non-Hamiltonian dynamics. At the same time, many questions remain open regarding structure-preserving, complexity, error analysis, and the practical relevance of these algorithms for concrete models arising in differential equations and applied analysis.
This minisymposium brings together researchers working at the interface of quantum algorithms, numerical analysis, and applications in physics and engineering. The talks will cover theoretical and methodological foundations of quantum algorithms, including algorithmic frameworks, complexity guarantees, stability and error analysis, and implementation-oriented perspectives.
Alongside methodological developments, the minisymposium will include illustrative applications that reflect the breadth of quantum scientific computing, such as quantum algorithms for lattice field theories and lattice gauge theories, and sampling-based quantum approaches to machine learning (including quantum annealing perspectives). The goal is to foster cross-disciplinary exchange, clarify the current state of the art, and identify problem classes with clear mathematical structure and practical relevance where quantum advantage may be achievable.

While classical numerical methods provide precision, stability, and strong theoretical guarantees, they can be computationally demanding and require problem-specific expertise. Recent advances in artificial intelligence (AI) have introduced data-driven, general-purpose models capable of efficient, flexible, and real-time scientific simulations. At the same time, many fundamental properties of AI models—such as stability, robustness, precision, and numerical reliability—remain less well understood than those of traditional algorithms.
This minisymposium highlights the growing role of AI as a transformative tool for scientific computing, while emphasizing the crucial contributions of numerical analysis in understanding and strengthening AI-based methods. Topics will include the use of AI to address challenges in numerical PDEs and scientific simulation, as well as the application of linear algebra, geometric analysis, and rounding error analysis to characterize and mitigate vulnerabilities in AI models

This mini-symposium will explore the intersection of optimization and ordinary or fractional differential equations, highlighting recent advances in analytical frameworks, numerical methods, and application-driven models. In particular, fractional operators have emerged as powerful tools in capturing memory, hereditary effects, and multiscale dynamics—making them natural candidates for modeling and solving complex optimization problems in science and engineering.The session will feature talks focusing on:

• Variational formulations involving integer or fractional derivatives;
• Optimal control of dynamical systems governed by ODEs or FDEs;
• Applications to real world problems.

The goal is to foster cross-disciplinary dialogue between researchers in optimization and numerical analysis, and to promote modeling and algorithmic tools for modern optimization tasks.

The multiscale dynamics occurring at interfaces and boundaries are of paramount importance in many scientific and industrial applications, such as fluid-structure interactions, free boundary material interfaces, and biological growth. With the advent of innovative numerical approaches based on evolving surfaces and geometric partial differential equations, the complex structures of a wide spectrum of phenomena can be preserved at the discrete level, and the numerical schemes can be implemented efficiently and accurately. This mini-symposium aims to discuss recent advances in the design, analysis and applications of numerical methods to moving interfacial problems, and geometric partial differential equations, among others.

Uncertainty quantification (UQ) in complex dynamical systems poses fundamental challenges in scientific computing, especially for high-dimensional, nonlinear ODE, PDE, and SDE/SPDE models. Recent advances in generative AI -- such as description models and score-based samplers -- offer new perspectives on approximating high-dimensional probability measures, constructing efficient sampling and filtering algorithms, and integrating noisy or partial observations with dynamical models. This mini-symposium will bring together researchers working at the interface of differential equations, numerical analysis, stochastic modeling, and generative AI. Contributions will include mathematically grounded developments of generative model-based UQ methods, training-free and structure-preserving description approaches, convergence and stability analyses, and applications to large-scale dynamical systems in science and engineering.

Advances in many fields like image recognition, natural language processing and also scientific computing, have in recent years been
driven by the application of neural networks. Neural networks are a class of non-linear functions that can in theory approximate any map to arbitrary accuracy. In practice they are almost always used to produce a fit to a data set, the so-called training data. Classical
numerics on the other hand is concerned with modeling differential equations on a computer to replicate analytic/physical behavior as
well as possible. Approximators used for this task are in many cases however very simple and are often only linear. In this minisymposium we want to go beyong the data-driven application of neural networks for scientific computing, and look at how existing techniques from classical numerics can be improved upon by incorporating more powerful nonlinear approximators, like neural networks.

Stochastic differential equations (SDEs) are an essential part of modern scientific computing, with various applications in Bayesian statistics, machine learning, optimal control, or molecular dynamics, to mention just a few examples. They provide a rich source of theoretical and algorithmic tools that can be used to analyse and improve the efficiency of Markov chain Monte Carlo, stochastic gradient descent, or the like. For typical sampling or learning tasks, the state or parameter space can have a complicated geometry or, as is common, the underlying probability measure is supported only on a low-dimensional submanifold. This is where SDEs with (algebraic) constraints come into play. This minisymposium will cover a number of different interconnected keywords arising in connection with constrained SDEs, such as

• diffusion models and sampling of conditional probabilities

• Markov chain Monte Carlo on submanifolds

• interpolation and fitting on Riemannian manifolds

• manifold hypothesis in statistical learning

• stochastic optimisation of functions defined on manifolds.

Today’s cutting-edge science and engineering simulations require the ability to highly resolve physical and temporal domains and to compute solutions to complex, multiphysics systems. Use of high performance computing platforms has been critical to progress in several application areas, including fusion and earth sciences, quantum physics, materials science, and health sciences. One significant insertion path for numerical mathematics innovations has been through their implementation in high performance software packages. In order to allow scientists and engineers to focus on their scientific challenges, numerical simulation frameworks commonly include interfaces to numerical packages. These interfaces provide access to libraries facilitating the inclusion of new algorithms and methods and achievement of high performance on today’s largest and most complex computing platforms. This minisymposium will include presentations on 4 numerical software libraries that facilitate the solution of complex scientific problems on today’s high performance computing platforms. The packages include the SUNDIALS library of time integrators and nonlinear solvers, the Firedrake system for solving partial differential equations with finite elements, the deal.II finite element library, and the MFEM library for finite element methods. Presentations will include overviews of the packages and their capabilities, as well as examples of their use on high performance systems.

Molecular Dynamics (MD) simulations provide atomistic-resolution information about equilibrium and dynamical properties of large-scale molecular systems, with numerous applications in biology, chemistry, materials science and engineering. Machine learning (ML) and artificial intelligence (AI) have provided exciting new ideas and tools to model molecular systems, to design simulation engines, or to analyse data from simulations. Prominent examples include AlphaFold2 and its successors, which enabled protein structure prediction at an unprecedented success rate, or machine-learned interatomic potentials (MLIPs), which enable evaluation of molecular energies at quantum-mechanical accuracy.
In this minisymposium, we aim to bring together researchers working on novel ML/AI-methods to predict molecular structures and properties, with a particular focus on dynamical quantities. We will hear state-of-the-art results on simulation of molecular systems using MLIPs, about AI-based learning of coarse-grained models, and about the use of generative models to overcome the sampling problem for molecular systems. The symposium is also meant to be a networking opportunity for young researchers, which is why all confirmed speakers are graduate students or junior postdocs.

Modeling high-dimensional and complex systems through partial differential equations has long been of interest in both industry and science. However, even as computational capabilities continue to advance, simulating such models remains highly challenging, particularly in tasks such as uncertainty quantification and inverse problems. Surrogate modeling has emerged as a widely studied research area, offering powerful approaches to reduce computational costs when dealing with very complex systems. In this minisymposium, we aim to bring together recent advances in surrogate modeling and to discuss the challenges the field faces. In particular, we focus on low-rank tensor methods, polynomial methods, scientific machine learning, and kernel-based methods.

Over the last few decades, fractional calculus has emerged as a powerful mathematical tool for describing complex systems characterized by memory effects, long-range dependencies, and anomalous transport phenomena across various fields. This minisymposium aims to provide researchers with the opportunity to exchange ideas and discuss key issues in the numerical solution of fractional ordinary differential equations and fractional partial differential equations, covering both the theoretical analysis of numerical methods and the strategies to reduce the high computational cost resulting from the non-local nature of the fractional operators. Contributions focusing on the application of numerical methods to specific problems from engineering, physics and other scientific disciplines, are also welcome.
As SciCADE is a prestigious international conference for presenting cutting- developments in scientific computing and in the numerical treatment of differential equations, this minisymposium is perfectly aligned with the conference's core themes. It provides a timely platform to address the specific computational challenges posed by fractional models within the broader scientific computing community.

Nonlinear transport equations arise in several applications and their numerical approximation requires advanced numerical methods, in particular in plasma physics. During this mini-symposium, we will have 4 talks dedicated to recent contributions on this keyword.

Implicit time stepping methods play a central role in the numerical solution of time dependent partial differential equations, particularly in stiff, multiscale, and highly nonlinear regimes. In many applications ranging from fluid dynamics and geophysical flows to plasma physics and materials science, explicit methods are severely constrained by stability restrictions. Fully implicit schemes offer the potential for robust simulations with large time steps. For large scale PDE models solved on parallel computers, the industry standard is semi-implicit methods, with the implicit part being chosen for efficient factorisation and re-use from one timestep to the next. However, recent advances in automated code generation as well as mathematics underpinning preconditioners are allowing us to consider fully implicit methods as a serious possibility for large scale PDE solution. This includes Galerkin-in-time methods and high order implicit collocation RK methods, for example.
This minisymposium will bring together recent advances in solution techniques for implicit time integration for PDEs, including their combination with structure-preserving spatial discretizations. In particular, many exactly conservative or energy-stable schemes naturally lead to nonlinear systems that must be solved iteratively at each time step, making efficient and scalable implicit solvers an essential component of the overall numerical method.
The minisymposium will highlight developments in algorithm design, analysis, and implementation of implicit time-stepping methods, including nonlinear solvers, preconditioning strategies, and interaction with modern spatial discretisations. We invite contributions addressing theoretical aspects, such as stability and convergence, as well as large-scale computational studies and applications, advancing the state of the art in implicit time integration and strengthen its role as a powerful tool for challenging PDE problems.

In the field of computational science, a central philosophy is that reliable and efficient numerical methods should preserve the underlying mathematical and physical structures of continuous problems. This principle has been highly successful in the development of Finite Element Exterior Calculus (FEEC), where the preservation of the de Rham complex at the discrete level has led to stable and efficient algorithms for electromagnetism and fluid dynamics.

However, many problems in physics and engineering, such as the Einstein equations in general relativity and the modeling of continua with complex microstructures, involve differential structures that go beyond the standard exterior calculus of differential forms. This minisymposium aims to explore the emerging framework of Finite Element Tensor Calculus (FETC). We will focus on the fundamental challenge of discretizing geometric objects and high-order tensor fields.

This session seeks to foster a unified framework for the modeling and computation of complex geometric PDEs, pushing the boundaries of what structure-preserving methods can achieve in scientific computing.

Interface problems arise in many areas of science and engineering, including multiphase flows, materials, electrostatics, and biology. This mini-symposium focuses on recent advances in numerical methods for partial differential equations with interfaces, covering theoretical analysis, algorithmic development, and practical applications. Applications to fluid dynamics, materials science, and biological systems will be highlighted. The goal is to provide a platform for exchanging ideas across disciplines, fostering collaboration, and advancing the state of the art in numerical methods for interface problems.

Machine learning methods for scientific computing have been increasingly popular in recent years. The aim of this minisymposium is to bring together researchers working with knowledge of machine learning for model discovery, physics-informed neural networks, operator learning, geometric deep learning, and numerical method for scientific computing to explore state-of-the-art development in the methodology of machine learning for scientific computing, in order to foster closer contact and facilitate the exchange of ideas and expertise across the different areas.

Active matter refers to systems whose constituents continuously inject energy locally—through self-propulsion or internal force generation—so that macroscopic behaviour cannot be understood as relaxation toward an equilibrium (Boltzmann) distribution. This non-equilibrium driving leads to striking collective phenomena such as flocking, swarming, spontaneous pattern formation, and turbulent flows. Canonical examples include bacterial suspensions, cytoskeletal and motor-protein networks, cell monolayers and tissues, and synthetic self-propelled colloids. For applied mathematicians, active matter is a fertile setting where stochasticity, transport, instabilities, and symmetry breaking are coupled in multiscale models connecting discrete “agents” to continuum fields.

This minisymposium focuses on computational methods for simulating and analysing active systems, and on the numerical challenges that distinguish them from passive soft matter. On the discrete side, we welcome work using agent-based particle models, molecular dynamics schemes, and Monte Carlo approaches to resolve interactions, propulsion mechanisms, and fluctuations. On the continuum side, we invite contributions on hydrodynamic simulations and numerical solution of PDE models for active matter. A complementary theme is data analysis: algorithms from computational geometry (e.g. neighbour/cluster detection, growth, and stochastic geometry) and diagnostic tools inspired by the physics of dense materials such as glasses.

Many scientific and engineering problems require estimating unknown parameters or states in dynamical systems from noisy, incomplete observations. These problems are often high-dimensional, ill-posed, and computationally demanding, requiring efficient numerical methods that can quantify uncertainties while remaining tractable for large-scale applications. Challenges include limited or noisy data, expensive forward models, nonlinear dynamics, and the need for scalable algorithms with rigorous error control.
This minisymposium will bring together researchers developing state-of-the-art numerical techniques for uncertainty quantification in inverse problems and data assimilation, as well as those applying these methods to complex real-world systems in areas such as geophysics, climate science, and engineering.

Iterative methods lie at the heart of modern scientific computing, providing efficient and scalable solvers for large-scale systems arising from the discretization of partial differential equations (PDEs) and related optimization problems. When solving such problems numerically, the complexity of the underlying phenomena, such as multiphysics formulation, high-frequency wave propagation, and long time scale, often requires extremely fine space and/or time discretizations, which leads to very large systems. Iterative solvers are among the most efficient methods to tackle this type of problem. This minisymposium focuses on recent developments in the design, analysis, and application of new iterative methods for both linear and non-linear problems. The talks will cover advances in classical frameworks such as domain decomposition, parallel-in-time methods, as well as novel preconditioning strategies and convergence acceleration techniques. Particular attention will be given to non-linear extensions, including modulus-based and fixed-point type iterations, where non-linearity introduces new analytical and computational challenges. The invited speakers will present theoretical insights into convergence behavior and robustness of iterative solvers, as well as algorithmic innovations adapted to parallel and time-dependent settings. The overall goal is to bring together experts working on different classes of iterative methods to exchange ideas and discuss associated open challenges in this research field.

Fluids and wave phenomena arise across a wide spectrum of scientific and engineering applications—from ocean dynamics, turbulences, acoustics, and electromagnetics to quantum physics and plasma models. Many of these systems are governed by partial differential equations whose solutions exhibit multiscale features, strong nonlinearities, geometric complexity, or oscillatory behavior. Achieving accurate and efficient numerical simulation of such problems remains a central challenge in computational mathematics and applied sciences.

Spectral and high-order methods play an increasingly important role in addressing these challenges. Their superior accuracy, excellent resolution properties, and ability to capture fine-scale structures with relatively few degrees of freedom make them especially attractive for modern large-scale simulations and emerging applications requiring high fidelity. At the same time, extending these methods to complex fluid and wave systems—whether through advanced discretizations, structure-preserving schemes, adaptivity, or efficient solvers—continues to drive active research.

This mini-symposium aims to bring together numerical analysts and computational scientists to present recent advances in the development, analysis, and application of spectral and high-order methods for fluid and wave problems. Topics include novel algorithmic developments, rigorous analysis, stabilization and structure-preserving techniques, and innovative applications to challenging PDE models in fluids, acoustics, electromagnetics, and beyond.

Partitioned time integration methods are designed to provide flexibility when evolving systems of differential equations that couple two or more physical processes in a single simulation. These combinations may include systems of differential equations with different type (parabolic, hyperbolic, etc.), with different degrees of nonlinearity, and that evolve on disparate time scales. As a result, such simulations can prove challenging for “monolithic” time integration methods that treat all processes using a single approach.

This mini-symposium focuses on the construction and analysis of new methods that move beyond the lowest-order operator splitting methods that have historically been applied to such problems. Through careful design, these algorithms are capable of tackling such applications with improved accuracy, stability, and/or computational efficiency than previously possible. This session features experts that focus on various families of partitioned integrators, including multi-rate, implicit-explicit, exponential, and stabilized explicit time integration methods.

This invited minisymposium will focus on recent research advances in several interrelated aspects of geometric and structure-preserving methods for numerical ODEs and PDEs. Topics include geometric integrators for dynamical systems and optimal control, structure-preserving methods in differential geometry and geometric PDEs, and methods that combine features of both of these for PDEs with geometric structure in both time and space.

SciCADE has long been a leading forum for research into these types of methods, and we look forward to continuing in this tradition. Additionally, we aim to bring together researchers from different branches of the structure-preserving numerical ODE and PDE communities who might interact less frequently in other settings.

The fields of stochastic dynamical systems and machine learning (ML) are undergoing a profound and synergistic convergence. This mini-symposium aims to explore this exciting interface, bringing together researchers from applied and computational mathematics, applied probability, and statistics . We will focus on how modern ML methods, such as generative models, transformers and neural networkss, are providing new tools for learning and simulating complex stochastic dynamics with applications to optimization, control, chemistry, physics, AI etc. Conversely, we will investigate how the rigorous framework of stochastic analysis is providing insights into the behavior and theoretical guarantees of ML models. Topics will include the stochastic particle systems as sampling algorithms, the use of ML for solving high-dimensional partial differential equations, and the dynamical view of deep learning and generative models, and the applications to scientific computing problems.

Generative models (GM), more precisely, estimation of distribution from data, have become a fundamental backbone in the field of Artificial Intelligence. In this minisymposium, we aim to explore the interaction between GM and differential equations. It includes how differential equation techniques can be applied to improve GM performance and provide theoretical guarantees. It also includes how the GMs could be used to address traditional challenging problems in the computation of differential equations.

Quantum algorithms offer asymptotic exponential speedups for two primitives central to differential-equation (DE) solvers: solving sparse linear systems and simulating Hamiltonian time evolution. Whether these speedups translate into end-to-end gains for ODE/PDE/SDE problems depends on concrete modeling choices and costs that are often glossed over. This minisymposium focuses on the technical bottlenecks and on strategies to mitigate them.

Different modeling choices for DEs affect end-to-end algorithmic costs and call for strategies to minimize their impact. Accordingly, understanding error scaling and convergence is central. Specifically, we propose to examine: (i) discretization strategies (spatial, spectral, etc.); (ii) linearization strategies (e.g., Carleman, Koopman); (iii) preconditioning strategies; (iv) efficient block encodings for discretized and linearized operators; and (v) data preparation and readout strategies.

Talks will present recent progress on such strategies and their compatibility with quantum primitives. Case studies will illustrate when these ingredients enable meaningful speedups for specific DEs (e.g., in fluid dynamics) under explicit input/output models. The goal is to delineate problems where advantage is plausible, make assumptions transparent, and distill design principles that yield realistic end-to-end performance.

The presence of moving interfaces is a fundamental challenge in a wide range of scientific and engineering applications, including fluid-structure interaction, multiphase flows, biological modeling, and material science. Traditional numerical methods often require remeshing or other computationally expensive techniques to adapt to the evolving geometry, making them less efficient for problems involving complex or dynamic interfaces. Unfitted finite element methods (FEM) offer a powerful alternative by allowing interfaces to be represented independently of the computational mesh. These methods provide significant advantages, including geometric flexibility, computational efficiency, and the ability to handle complex interface dynamics without compromising accuracy. This minisimposium will bring together researchers working on the development, analysis, and application of unfitted FEM for problems involving moving interfaces. The aim is to provide a platform to present recent advances in this field, foster discussion on theoretical and computational challenges, and explore new directions for research and applications.

Neural networks are increasingly reshaping scientific computing, providing powerful tools to numerically approximate PDE solutions, learn surrogate models, and accelerate PDE solvers. This minisymposium at SciCADE 2026 will highlight recent advances in the analysis and algorithms of neural-network-based methods for PDE-driven forward and inverse problems, with particular emphasis on approximation and expressivity theory (including Barron-type spaces and related function-space perspectives), optimization and generalization under physics-based constraints, and efficient learning architectures. By bringing together researchers from computational mathematics, numerical PDEs, and machine learning, the session aims to foster a focused exchange on rigorous theory, practical algorithms, and emerging directions at the interface of deep learning and PDEs.

Machine learning methods for scientific computing have been increasingly popular in recent years. The aim of this minisymposium is to bring together researchers working with knowledge of machine learning for model discovery, physics-informed neural networks, operator learning, geometric deep learning, and numerical method for scientific computing to explore state-of-the-art development in the methodology of machine learning for scientific computing, in order to foster closer contact and facilitate the exchange of ideas and expertise across the different areas.

Active matter refers to systems whose constituents continuously inject energy locally—through self-propulsion or internal force generation—so that macroscopic behaviour cannot be understood as relaxation toward an equilibrium (Boltzmann) distribution. This non-equilibrium driving leads to striking collective phenomena such as flocking, swarming, spontaneous pattern formation, and turbulent flows. Canonical examples include bacterial suspensions, cytoskeletal and motor-protein networks, cell monolayers and tissues, and synthetic self-propelled colloids. For applied mathematicians, active matter is a fertile setting where stochasticity, transport, instabilities, and symmetry breaking are coupled in multiscale models connecting discrete “agents” to continuum fields.

This minisymposium focuses on computational methods for simulating and analysing active systems, and on the numerical challenges that distinguish them from passive soft matter. On the discrete side, we welcome work using agent-based particle models, molecular dynamics schemes, and Monte Carlo approaches to resolve interactions, propulsion mechanisms, and fluctuations. On the continuum side, we invite contributions on hydrodynamic simulations and numerical solution of PDE models for active matter. A complementary theme is data analysis: algorithms from computational geometry (e.g. neighbour/cluster detection, growth, and stochastic geometry) and diagnostic tools inspired by the physics of dense materials such as glasses.

Many scientific and engineering problems require estimating unknown parameters or states in dynamical systems from noisy, incomplete observations. These problems are often high-dimensional, ill-posed, and computationally demanding, requiring efficient numerical methods that can quantify uncertainties while remaining tractable for large-scale applications. Challenges include limited or noisy data, expensive forward models, nonlinear dynamics, and the need for scalable algorithms with rigorous error control.
This minisymposium will bring together researchers developing state-of-the-art numerical techniques for uncertainty quantification in inverse problems and data assimilation, as well as those applying these methods to complex real-world systems in areas such as geophysics, climate science, and engineering.

Partial differential equations posed on moving domains and evolving surfaces arise naturally in many areas of science and engineering, including fluid–structure interaction, free-boundary and multiphase flows, geometric flows, and biological membrane dynamics. These problems frequently involve moving or deforming interfaces, curvature-related terms and coupled bulk–surface processes. The geometric evolution introduces substantial analytical and numerical challenges, such as establishing stability and convergence of discretizations of these nonlinear problems, and maintaining mesh quality under large deformations.

This minisymposium brings together researchers developing advanced numerical methods and the numerical analysis for PDEs on evolving geometries. Topics include evolving surface finite element methods, curvature-driven flows, bulk–surface coupled problem, and free-boundary and fluid–structure interaction problems.

By fostering interaction among experts in numerical analysis and scientific computing, this minisymposium will highlight recent progress, identify emerging analytical and computational challenges, and promote new directions for the simulation of PDEs on moving domains and evolving surfaces.

Fluids and wave phenomena arise across a wide spectrum of scientific and engineering applications—from ocean dynamics, turbulences, acoustics, and electromagnetics to quantum physics and plasma models. Many of these systems are governed by partial differential equations whose solutions exhibit multiscale features, strong nonlinearities, geometric complexity, or oscillatory behavior. Achieving accurate and efficient numerical simulation of such problems remains a central challenge in computational mathematics and applied sciences.

Spectral and high-order methods play an increasingly important role in addressing these challenges. Their superior accuracy, excellent resolution properties, and ability to capture fine-scale structures with relatively few degrees of freedom make them especially attractive for modern large-scale simulations and emerging applications requiring high fidelity. At the same time, extending these methods to complex fluid and wave systems—whether through advanced discretizations, structure-preserving schemes, adaptivity, or efficient solvers—continues to drive active research.

This mini-symposium aims to bring together numerical analysts and computational scientists to present recent advances in the development, analysis, and application of spectral and high-order methods for fluid and wave problems. Topics include novel algorithmic developments, rigorous analysis, stabilization and structure-preserving techniques, and innovative applications to challenging PDE models in fluids, acoustics, electromagnetics, and beyond.

Partitioned time integration methods are designed to provide flexibility when evolving systems of differential equations that couple two or more physical processes in a single simulation. These combinations may include systems of differential equations with different type (parabolic, hyperbolic, etc.), with different degrees of nonlinearity, and that evolve on disparate time scales. As a result, such simulations can prove challenging for “monolithic” time integration methods that treat all processes using a single approach.

This mini-symposium focuses on the construction and analysis of new methods that move beyond the lowest-order operator splitting methods that have historically been applied to such problems. Through careful design, these algorithms are capable of tackling such applications with improved accuracy, stability, and/or computational efficiency than previously possible. This session features experts that focus on various families of partitioned integrators, including multi-rate, implicit-explicit, exponential, and stabilized explicit time integration methods.

Splitting methods form a popular class of numerical integrators, particularly well suited for differential equations (either ordinary or partial) that can be subdivided into different problems easier to solve than the original system. Efficient high-order schemes have been designed along the years that provide accurate
solutions whilst preserving some of the most salient qualitative features of the system they approximate. These methods possess a number of features which make them a versatile strategy in the treatment of a number of problems arising from many different applications. In fact, splitting methods are extensively used in areas as distant as molecular dynamics, particle accelerators, celestial mechanics, quantum (statistical) mechanics, plasma physics, hydrodynamics and Markov chain Monte Carlo methods (see surveys [1] and [2]).

The purpose of this mini symposium is to showcase recent advances in the realm of splitting methods, with special emphasis on innovative applications across different areas of interest. Topics include the treatment of wave propagation in nonlinear dispersive media, reaction-diffusion partial differential equations, the time evolution of quantum mechanical problems and quantum simulations using quantum computers. To this end, four distinguished experts have been invited to present their latest research.

References:

[1] R.I. McLachlan and R. Quispel. Splitting methods. Acta Numerica 11 (2002), 341-434.
[2] S. Blanes, F. Casas, and A. Murua. Splitting methods for differential equations. Acta Numerica 33 (2024), 1-161.

This invited minisymposium will focus on recent research advances in several interrelated aspects of geometric and structure-preserving methods for numerical ODEs and PDEs. Topics include geometric integrators for dynamical systems and optimal control, structure-preserving methods in differential geometry and geometric PDEs, and methods that combine features of both of these for PDEs with geometric structure in both time and space.

SciCADE has long been a leading forum for research into these types of methods, and we look forward to continuing in this tradition. Additionally, we aim to bring together researchers from different branches of the structure-preserving numerical ODE and PDE communities who might interact less frequently in other settings.

Quantum algorithms offer asymptotic exponential speedups for two primitives central to differential-equation (DE) solvers: solving sparse linear systems and simulating Hamiltonian time evolution. Whether these speedups translate into end-to-end gains for ODE/PDE/SDE problems depends on concrete modeling choices and costs that are often glossed over. This minisymposium focuses on the technical bottlenecks and on strategies to mitigate them.

Different modeling choices for DEs affect end-to-end algorithmic costs and call for strategies to minimize their impact. Accordingly, understanding error scaling and convergence is central. Specifically, we propose to examine: (i) discretization strategies (spatial, spectral, etc.); (ii) linearization strategies (e.g., Carleman, Koopman); (iii) preconditioning strategies; (iv) efficient block encodings for discretized and linearized operators; and (v) data preparation and readout strategies.

Talks will present recent progress on such strategies and their compatibility with quantum primitives. Case studies will illustrate when these ingredients enable meaningful speedups for specific DEs (e.g., in fluid dynamics) under explicit input/output models. The goal is to delineate problems where advantage is plausible, make assumptions transparent, and distill design principles that yield realistic end-to-end performance.

Mathematical modeling provides powerful tools for investigating the complexity of environmental systems, where interactions among vegetation, soil processes, climate variability, and natural disturbances shape ecosystem dynamics. These interactions can generate short- or long-term transitions between alternative states. Models describing such phenomena across scales uncover aspects of stability, sensitivity to noise and parameter shifts.
Sudden loss of stability may induce critical shifts between different ecological regimes. Relevant keywords include the emergence of patterns in ecological and soil systems, population dynamics under environmental drivers, and the impact of disturbances, such as fire, on landscape transitions.
This minisymposium will bring together contributions that employ advanced mathematical modeling and computational approaches to address these challenges. Mathematical modeling helps in understanding environmental processes, whether through classical differential equations frameworks, agent-based systems, or novel data-driven models, with the aim of supporting management decision-making and promoting sustainable development.
Traditional numerical methods often struggle to accurately reproduce the solutions of such complex models, requiring specialized techniques tailored to each problem. In particular, the high dimensionality of environmental systems and the large amount of real world data frequently require model order reduction strategies or data driven computational methods.
By bridging theoretical aspects with algorithmic developments, this minisymposium aims to foster discussion on how mathematics can shed light on environmental complexity and enhance our understanding of ecosystem responses to changing conditions.

The presence of moving interfaces is a fundamental challenge in a wide range of scientific and engineering applications, including fluid-structure interaction, multiphase flows, biological modeling, and material science. Traditional numerical methods often require remeshing or other computationally expensive techniques to adapt to the evolving geometry, making them less efficient for problems involving complex or dynamic interfaces. Unfitted finite element methods (FEM) offer a powerful alternative by allowing interfaces to be represented independently of the computational mesh. These methods provide significant advantages, including geometric flexibility, computational efficiency, and the ability to handle complex interface dynamics without compromising accuracy. This minisimposium will bring together researchers working on the development, analysis, and application of unfitted FEM for problems involving moving interfaces. The aim is to provide a platform to present recent advances in this field, foster discussion on theoretical and computational challenges, and explore new directions for research and applications.

Neural networks are increasingly reshaping scientific computing, providing powerful tools to numerically approximate PDE solutions, learn surrogate models, and accelerate PDE solvers. This minisymposium at SciCADE 2026 will highlight recent advances in the analysis and algorithms of neural-network-based methods for PDE-driven forward and inverse problems, with particular emphasis on approximation and expressivity theory (including Barron-type spaces and related function-space perspectives), optimization and generalization under physics-based constraints, and efficient learning architectures. By bringing together researchers from computational mathematics, numerical PDEs, and machine learning, the session aims to foster a focused exchange on rigorous theory, practical algorithms, and emerging directions at the interface of deep learning and PDEs.

Generative models are increasingly central to scientific machine learning for surrogate modeling, inverse problems, uncertainty quantification, and data assimilation. However, in the low-data, highly structured regimes typical of science and engineering, training can be unstable and model selection difficult to justify. This minisymposium focuses on principled generative modeling, meaning mathematically grounded theory and algorithms that make generative models faster to train, more robust, and more data-efficient for scientific machine learning (SciML) applications. A key direction in this area is to combine variational learning induced by novel divergences with methods that take advantage of structured probabilistic representations.

The minisymposium will highlight three interconnected threads spanning both principled training and principled model design. The first concerns learning objectives based on novel information divergences, including optimal-transport-inspired, interpolative, and regularized divergences, with an emphasis on stable training and ways to incorporate side information. The second examines learning through the lens of training dynamics, such as operator learning and proximal or regularized schemes for gradient flows that connect optimization with transport and PDE perspectives. The third emphasizes learning probabilistic graphical modeling, including Bayesian networks and Markov random fields, as a principled route to encoding hierarchy, sparsity, and conditional independence.

The proposed talks bridge two or more of these threads, aiming to develop a coherent set of ideas for building and training efficient and reliable generative SciML surrogates that respect scientific structure while delivering practical gains and improving stability, sample efficiency, and performance.

Scientific Machine Learning (SciML) has emerged as a powerful paradigm to combine the expressiveness and adaptability of machine learning with the robustness and interpretability of physics-based models. This mini-symposium focuses on hybrid and structure-preserving methods that tightly integrate traditional numerical solvers, reduced-order models, and neural networks within unified computational frameworks. Here, “hybrid” also refers to approaches in which key mathematical or physical properties of the underlying PDEs or numerical schemes — such as conservation, stability, or invariants — are embedded directly into the learned models themselves. The goal of such hybridization is not only to accelerate simulations or improve predictive accuracy, but also to retain the mathematical guarantees, physical consistency, and numerical stability that are essential in scientific and engineering contexts.

We invite contributions exploring, among others: differentiable solvers and PDE-constrained learning, neural operators and physics-informed architectures, structure-preserving neural models, coupling of HPC codes with machine-learned surrogates, and adaptive hybrid schemes leveraging physical priors or conservation laws. A particular emphasis will be placed on approaches that ensure provable convergence, bounded errors, and interpretable behavior when data-driven components are embedded within deterministic solvers. The symposium will also address key challenges such as scalability on modern hardware, trade-offs between accuracy and computational speed-up, uncertainty quantification, long-term stability, and guarantees of structure preservation — all central to the reliable deployment of SciML methods in real-world high-performance computing environments.

Recent advances in computational mechanics indicate that certain discretisations can be regarded as intrinsic in a mathematical sense, as they emerge naturally from principles of conformity, well-posedness, or regularity. By drawing on classical functional analysis or leveraging modern concepts such as structure preservation through Hilbert space complexes, it is possible to systematically construct such discretisations while enforcing physics-based constraints a priori. This approach ensures that numerical simulations remain faithful to the underlying physics while maintaining robustness and stability.

This minisymposium aims to explore the breadth and depth of current research on intrinsic discretisations within computational mechanics. It seeks to bring together researchers and practitioners from diverse domains to discuss theoretical advances, application-driven challenges, and opportunities for further development.

Low-rank tensor and matrix decompositions have become indispensable tools for extracting meaningful structure from high-dimensional data across science and engineering. By representing complex data in compact, structured forms, these methods offer computationally efficient and mathematically interpretable tools for data understanding. This session brings together contributions spanning the algorithmic foundations and applied frontiers of low-rank methods. On the algorithmic side, topics include optimization challenges inherent to tensor decompositions and strategies to overcome them, as well as the use of tensor decompositions as flexible compressed representations for both supervised and unsupervised machine learning. On the application side, low-rank models can be tailored to incorporate domain-specific structure — such as conservation laws in numerical simulation or rhythmic repetition in music audio — yielding richer and more faithful reduced representations. The session highlights the breadth of low-rank decomposition methods across diverse domains including signal processing, scientific computing, and data-driven machine learning.

The minisymposium focuses on recent advances in the numerical approximation of deterministic and stochastic dynamical systems. Alongside the analysis of modern challenges in achieving efficient and accurate solutions, the symposium addresses current developments and research directions such as structure-preserving integration, non-standard time integration, positivity preservation and scientific machine learning. The talks will cover both theoretical aspects of numerical modelling and selected applications.

Machine learning is increasingly used to accelerate scientific computing, but its impact in numerical simulations depends on methods that remain numerically reliable. This minisymposium focuses on hybrid approaches that embed learnable components into classical solvers, e.g., learned preconditioners or adaptive meshing strategies, while preserving the ability to analyse convergence, stability, and accuracy. The keyword is timely: it links data-informed algorithm design to the theoretical aspects of numerical methods for differential equations, targeting contemporary large-scale, multiscale, and high-dimensional regimes in which classical methods may fail due to computational complexity.

Machine learning, particularly neural networks, has demonstrated remarkable capabilities in solving tasks across various domains. The study of their value in scientific computing is emerging. There is great potential in developing hybrid numerical methods that inherit the desirable theoretical guarantees of classical solvers, while improving upon them through the efficiency and flexibility of machine learning models.

This mini-symposium gathers recent contributions on the design of numerical methods coupled with machine learning that remain amenable to theoretical analysis of their convergence, stability, and accuracy. We gather contributions that focus on both iterative solvers for linear systems and methods for differential equations.

The minisymposium features talks about current advances in dynamical cores in numerical weather prediction. These can be related to demands coming with a higher resolution or about the interplay of new data driven approaches with classical physics based ones. The equations solved are the three-dimensional Euler equations, or a simplified variant, formulated on the sphere and supplemented with gravitational source terms and possibly subgrid-scale parameterizations such as turbulence. Examples for keywords are high order methods, high performance computing, stability, computations on the sphere, efficient time integration methods, and physically-inspired data-driven methods.

We believe that this minisymposium fits the themes of the conference very well, touching on numerical weather prediction and climate science, and using methods from the PDE world.

The fields of stochastic dynamical systems and machine learning (ML) are undergoing a profound and synergistic convergence. This mini-symposium aims to explore this exciting interface, bringing together researchers from applied and computational mathematics, applied probability, and statistics . We will focus on how modern ML methods, such as generative models, transformers and neural networkss, are providing new tools for learning and simulating complex stochastic dynamics with applications to optimization, control, chemistry, physics, AI etc. Conversely, we will investigate how the rigorous framework of stochastic analysis is providing insights into the behavior and theoretical guarantees of ML models. Topics will include the stochastic particle systems as sampling algorithms, the use of ML for solving high-dimensional partial differential equations, and the dynamical view of deep learning and generative models, and the applications to scientific computing problems.

Coarse-graining atomistic systems enables the scalability of computer simulations of molecular systems to time and length scales that are computationally infeasible for atom-level molecular dynamics simulations, yet necessary for uncovering collective and emergent phenomena common, for example, in the conformational dynamics of biomolecules. While coarse-graining of atomistic systems has been an active research field for decades, recent advances in machine learning approaches have opened new avenues for designing and implementing coarse-graining methods.

This minisymposium will bring together researchers working on coarse-graining theory and applications, or on machine learning methods relevant to the development of the next generation of coarse-graining methods, including stochastic generative models and geometric (deep) learning. A particular focus and aim of the mini-symposium is to stimulate discussions and collaborations on developing new methods for dynamics-preserving coarse-grained representations and (automated) learning of coarse-grained representations.

This mini-symposium will focus on advanced numerical methods for addressing the quantum many-body problem, a pivotal challenge in quantum optics, materials science, and quantum chemistry. The intrinsic complexity of the quantum many-body problem, characterized by its high degrees of freedom, presents a significant computational challenge that has driven extensive theoretical and methodological advancements over the past several decades. The importance of this keyword is underscored by the substantial allocation of global supercomputing resources to chemistry and materials simulations. According to the Swiss National Supercomputing Centre, approximately 35% of their computational resources are devoted to these areas, reflecting the critical role that numerical methods play in advancing research in these fields.

The goal of this mini-symposium is to provide a platform for promising young scientists from leading research groups to engage in discussions on recent theoretical and computational advancements in state-of-the-art approaches to the quantum many-body problem. By fostering dialogue and collaboration among researchers with diverse areas of expertise, the symposium aims to promote the exchange of ideas and encourage cross-fertilization between different research disciplines, ultimately driving forward innovation and progress in this critical field.

High-dimensional partial differential equations (PDEs) arise in various critical fields—from quantum physics, rarefied gas dynamics, and radiative transfer to plasma physics and the modeling of particle systems. However, due to the curse of dimensionality, efficient numerical simulation of such systems remains challenging.

In recent years, significant progress has been made toward mitigating even overcoming the curse of dimensionality in the simulation of these PDEs through the development of dimensionality reduction and low-rank methods. These include data-driven reduced-order models, rank-adaptive techniques, dynamical low-rank algorithms, and step-and-truncate algorithms. This minisymposium seeks to bring together researchers working on these and related approaches, with the goal of sharing recent advances, fostering cross-disciplinary and international collaboration, and promoting the exchange of innovative ideas in the scientific computing and numerical analysis of high-dimensional PDEs.

This minisymposium deals with structure-preserving machine learning, in particular in the context of differential-algebraic equations (DAEs) and (port-)Hamiltonian systems. Both DAEs and (port-)Hamiltonian systems arise when modeling physical phenomena that possess some underlying structure. For instance, they can appear in the contexts of electrical circuits, abstract flow networks or when working with conservation laws more generally. In each of these examples, the underlying structure, think e.g. Kirchhoff's laws, leads to (hidden) constraints that describe the physically admissible states of the system. Thus it becomes important to understand how to correctly incorporate these constraints into machine learning workflows, to ensure that predictions also satisfy them.

The minisymposium features talks about current advances in dynamical cores in numerical weather prediction. These can be related to demands coming with a higher resolution or about the interplay of new data driven approaches with classical physics based ones. The equations solved are the three-dimensional Euler equations, or a simplified variant, formulated on the sphere and supplemented with gravitational source terms and possibly subgrid-scale parameterizations such as turbulence. Examples for keywords are high order methods, high performance computing, stability, computations on the sphere, efficient time integration methods, and physically-inspired data-driven methods.

We believe that this minisymposium fits the themes of the conference very well, touching on numerical weather prediction and climate science, and using methods from the PDE world.