Operator inference for non-intrusive model reduction with quadratic manifolds
Abstract
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.
- Authors:
-
- Univ. of Texas, Austin, TX (United States). Oden Institute for Computational Engineering and Sciences
- Univ. of Wisconsin, Madison, WI (United States)
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States). Oden Institute for Computational Engineering and Sciences; Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE; US Air Force Office of Scientific Research (AFOSR)
- OSTI Identifier:
- 1905877
- Alternate Identifier(s):
- OSTI ID: 1899717; OSTI ID: 2340144
- Grant/Contract Number:
- SC0019303; FA9550-21-1-0084
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 403; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Data-driven model reduction; Nonlinear manifolds; Operator inference; Proper orthogonal decomposition
Citation Formats
Geelen, Rudy, Wright, Stephen, and Willcox, Karen. Operator inference for non-intrusive model reduction with quadratic manifolds. United States: N. p., 2022.
Web. doi:10.1016/j.cma.2022.115717.
Geelen, Rudy, Wright, Stephen, & Willcox, Karen. Operator inference for non-intrusive model reduction with quadratic manifolds. United States. https://doi.org/10.1016/j.cma.2022.115717
Geelen, Rudy, Wright, Stephen, and Willcox, Karen. Sat .
"Operator inference for non-intrusive model reduction with quadratic manifolds". United States. https://doi.org/10.1016/j.cma.2022.115717. https://www.osti.gov/servlets/purl/1905877.
@article{osti_1905877,
title = {Operator inference for non-intrusive model reduction with quadratic manifolds},
author = {Geelen, Rudy and Wright, Stephen and Willcox, Karen},
abstractNote = {This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.},
doi = {10.1016/j.cma.2022.115717},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = ,
volume = 403,
place = {United States},
year = {Sat Nov 19 00:00:00 EST 2022},
month = {Sat Nov 19 00:00:00 EST 2022}
}
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