Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Sawant, Nihar; Kramer, Boris; Peherstorfer, Benjamin

doi:10.1016/j.cma.2022.115836

Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Journal Article · Sat Dec 17 00:00:00 EST 2022 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2022.115836· OSTI ID:2421165

Sawant, Nihar ^[1]; ^[2]; Peherstorfer, Benjamin ^[3]

New York Univ. (NYU), NY (United States); OSTI
Univ. of California, San Diego, CA (United States)
New York Univ. (NYU), NY (United States)

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). Here, this work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.

View Accepted Manuscript (DOE)

Research Organization:: New York Univ. (NYU), NY (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0019334

OSTI ID:: 2421165

Alternate ID(s):: OSTI ID: 1906749

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 404; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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