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

Abstract

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.

Authors:

Benner, Peter ^[1]; Goyal, Pawan  ^[1];

• Search DOE PAGES for author "Goyal, Pawan"
• Search DOE PAGES for ORCID "0000-0003-3072-7780"

Kramer, Boris  ^[2];

• Search DOE PAGES for author "Kramer, Boris"
• Search DOE PAGES for ORCID "0000-0002-3626-7925"

Peherstorfer, Benjamin ^[3]; Willcox, Karen ^[4]

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+ Show Author Affiliations

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

Publication Date:

Wed Oct 07 00:00:00 EDT 2020

Research Org.:

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

Sponsoring Org.:

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

OSTI Identifier:

1853047

Alternate Identifier(s):

OSTI ID: 1670814

Grant/Contract Number:  

SC0019303; SC0019334; FA9550-17-1-0195; FA9550-15-1-0038; FA9550-18-1-0023; 1901091

Resource Type:

Accepted Manuscript

Journal Name:

Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:

Journal Volume: 372; Journal Issue: C; Journal ID: ISSN 0045-7825

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; model reduction; data-driven modeling; nonlinear dynamical systems; scientific machine learning; operator inference