Surrogate Modeling for Physical Systems with Preserved Properties and Adjustable Tradeoffs

TL;DR

This paper introduces a flexible surrogate modeling framework for physical systems that balances simulation cost and accuracy, using both model-based and data-driven approaches with property preservation.

Contribution

It presents a novel framework combining model order reduction and data-driven methods to generate interpretable and stable surrogate models with adjustable tradeoffs.

Findings

Provides a model-based MOR approach with error bounds and stability

Develops a data-driven method using Tonti diagrams for interpretability

Supports various discretization schemes for diverse physics applications

Abstract

Determining the proper level of details to develop and solve physical models is usually difficult when one encounters new engineering problems. Such difficulty comes from how to balance the time (simulation cost) and accuracy for the physical model simulation afterwards. We propose a framework for automatic development of a family of surrogate models of physical systems that provide flexible cost-accuracy tradeoffs to assist making such determinations. We present both a model-based and a data-driven strategy to generate surrogate models. The former starts from a high-fidelity model generated from first principles and applies a bottom-up model order reduction (MOR) that preserves stability and convergence while providing a priori error bounds, although the resulting reduced-order model may lose its interpretability. The latter generates interpretable surrogate models by fitting artificial constitutive relations to a presupposed topological structure using experimental or simulation data. For the latter, we use Tonti diagrams to systematically produce differential equations from the assumed topological structure using algebraic topological semantics that are common to various lumped-parameter models (LPM). The parameter for the constitutive relations are estimated using standard system identification algorithms. Our framework is compatible with various spatial discretization schemes for distributed parameter models (DPM), and can supports solving engineering problems in different domains of physics.