Pankaj Chouhan - Dissertation Defense
"Surrogate Modeling with Gaussian Processes for Molecular Models of Viscoelasticity"
422 DSL (+ via Zoom)
Abstract:
In the polymer industry, physics-based computational molecular models serve as a tool for optimizing product quality and improving manufacturing processes. Molecular models of polymer dynamics take the molecular composition of a polymer mixture as input and yield the linear or nonlinear viscoelasticity properties of the mixture as output. These models come in different flavors offering different tradeoffs between accuracy and speed. For some applications where these models are evaluated repeatedly, for example in a Bayesian inverse problem setting, the cumulative computational cost of molecular simulations can be prohibitive. This is where surrogate models can help. Surrogate models (SMs) approximate the input-output behavior of molecular models at a fraction of the computational cost.
This work explores building SMs for a class of molecular models of polymer dynamics. These models yield the stress relaxation spectrum (RS) -- a fundamental property that describes the viscoelasticity of polymer mixtures. The SMs considered in this dissertation are based on Gaussian processes (GPs). GPs are non-parametric non-linear regression techniques with several appealing features. They offer the promise of well-calibrated predictions combined with uncertainty quantification. They allow for incorporation of prior information through kernel functions, interpolate training data, perform well for sparse data, and offer a natural framework for handling functional data.
This dissertation makes two contributions of significance. The first contribution is the development of a SM using a separable kernel-based GP. This SM accurately captures the mapping of the underlying molecular model. We successfully demonstrate its application in solving an inverse problem within a Bayesian framework. The second contribution of this dissertation is the development of SMs for limited functional data (100 samples) using reduced-order modeling. We explore two different datasets corresponding to two distinct molecular models. One of the datasets exhibits sharp features, while the other is relatively smooth. Reduced order SMs accurately capture the mapping of the underlying molecular model for smooth data, while struggling on datasets with sharp features.