Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraints
This work addresses the challenge of maintaining physical constraints in predictive modeling for scientific machine learning, offering an incremental enhancement to existing Operator Inference methods.
The paper tackles the problem of ensuring physical consistency and stability in reduced-order models for complex multiphysics systems like char combustion, by embedding state constraints into Operator Inference, resulting in improved stability and accuracy that extrapolates over 200% beyond the training regime.
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.