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

2025-02-05

AI Summary

This work addresses instability and poor extrapolation in standard operator inference (OpInf) for model reduction of multiphysics systems—such as carbon combustion—where state variables must satisfy physical constraints (e.g., non-negativity, conservation laws). We propose a physics-constrained OpInf framework that systematically embeds hard physical constraints into the learning process. Key contributions include: (i) the first systematic incorporation of hard state constraints into OpInf optimization; and (ii) a performance-driven, adaptive regularization hyperparameter selection strategy. Evaluated on high-fidelity carbon combustion simulations, the method significantly enhances long-term stability and physical consistency, achieving extrapolation beyond 200% of the training domain. It outperforms standard OpInf and leading stabilization approaches in both accuracy and robustness, while retaining computational efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Enhancing Operator Inference with state constraints
• Improving stability and accuracy in reduced-order modeling
• Extending predictive capabilities beyond training regime

Innovation

• Enhances Operator Inference with constraints
• Chooses regularization hyperparameters uniquely
• Ensures model stability and accuracy