Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraints

TL;DR

This paper introduces a method to improve reduced-order models of complex systems by embedding physical state constraints into Operator Inference, enhancing stability, accuracy, and extrapolation capabilities.

Contribution

It proposes a novel way to incorporate physical state constraints into Operator Inference, improving model stability and predictive accuracy for complex multiphysics systems.

Findings

Enhanced stability of reduced-order models with state constraints

Superior accuracy and physical consistency in char combustion simulations

Model extrapolates over 200% beyond training data

Abstract

Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference -- a methodology within scientific machine learning that enables learning from data a low-dimensional representation of a high-dimensional system governed by nonlinear partial differential equations -- by embedding such state constraints in the reduced-order model predictions. In the model learning process, we propose a new way to choose regularization hyperparameters based on a key performance indicator. Since embedding state constraints improves the stability of the Operator Inference reduced-order model, we compare the proposed state constraints-embedded Operator Inference with the standard Operator Inference and other stability-enhancing approaches. For an application to char combustion, we demonstrate that the proposed approach yields state predictions superior to the other methods regarding stability and accuracy. It extrapolates over 200\% past the training regime while being computationally efficient and physically consistent.