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

• URL: http://arxiv.org/abs/2502.03672v1
• Date: Wed, 05 Feb 2025 23:33:31 GMT
• Title: Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraints
• Authors: Hyeonghun Kim, Boris Kramer,
• Abstract summary: This paper presents a new approach to augment Operator Inference by embedding state constraints in reduced-order model predictions. For an application to char combustion, we demonstrate that the proposed approach yields state predictions superior to the other methods regarding stability and accuracy.
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• 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.

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