Tags:Calibration, Coarse-Grained Molecular Dynamics and Uncertainty Quantification
Abstract:
The validation of simulation models is typically achieved through the calibration of a set of unknown but fixed modeling parameters. However, such a perspective neglects the functional dependence of the calibration parameters on the modeling variables. Being able to learn this functional dependence would bring about more generalizable models and enable inference into unknown physical phenomenon. Learning these functional dependencies involves a nonisometric surface matching of a low-fidelity model to a lower-dimensional high-fidelity response surface. Available methods require modelers to specify the functional form of the calibration functions a priori or adopt a Bayesian approach that scales poorly with an increased number of input dimensions. In this work, we propose an adaptive sampling scheme that makes sequential inference into the eigenvectors of the covariance matrix of the calibration function parameters through a singular value decomposition by optimization of the likelihood function with a constant learning rate. The quantified uncertainty provides modeling support when selecting the functional form of the calibration functions. The validity of the method is demonstrated by calibrating a coarse-grained epoxy model with eight responses (Debye-Waller factor, Density, Modulus and Yield strength for two curing agents), one design variable (degree of crosslinking), and 14 unknown forcefield calibration functions.
Uncertainty Quantification in Functional Model Calibration: an Application in Coarse-Grained Epoxy Models