Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

Benner, Peter; Goyal, Pawan; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen

doi:10.1016/j.cma.2020.113433

Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

Journal Article · Wed Oct 07 00:00:00 EDT 2020 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.113433· OSTI ID:1853047

Benner, Peter ^[1]; ^[2]; ^[3]; Peherstorfer, Benjamin ^[4]; Willcox, Karen ^[5]

Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg (Germany); Univ. of California, San Diego, CA (United States)
Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg (Germany)
Univ. of California, San Diego, CA (United States)
New York Univ. (NYU), NY (United States)
Univ. of Texas, Austin, TX (United States)

Here in this work we present a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion–reaction Chafee–Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.

View Accepted Manuscript (DOE)

Research Organization:: New York Univ. (NYU), NY (United States); Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); US Air Force Center of Excellence; USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0019303; SC0019334

OSTI ID:: 1853047

Alternate ID(s):: OSTI ID: 1670814

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 372; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Toward fitting structured nonlinear systems by means of dynamic mode decomposition Gosea, Ion Victor; Duff, Igor Pontes arXiv https://doi.org/10.48550/arxiv.2003.06484	preprint	January 2020
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