Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations
Abstract
In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of themore »
- Authors:
-
- University of Texas, Austin, TX (United States)
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1976972
- Alternate Identifier(s):
- OSTI ID: 1840636
- Grant/Contract Number:
- SC0019303
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 389; Journal Issue: C; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; nonlinear model reduction; lifting transformations; differential–algebraic equation; operator inference; additive manufacturing; solidification
Citation Formats
Khodabakhshi, Parisa, and Willcox, Karen E. Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations. United States: N. p., 2021.
Web. doi:10.1016/j.cma.2021.114296.
Khodabakhshi, Parisa, & Willcox, Karen E. Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations. United States. https://doi.org/10.1016/j.cma.2021.114296
Khodabakhshi, Parisa, and Willcox, Karen E. Sat .
"Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations". United States. https://doi.org/10.1016/j.cma.2021.114296. https://www.osti.gov/servlets/purl/1976972.
@article{osti_1976972,
title = {Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations},
author = {Khodabakhshi, Parisa and Willcox, Karen E.},
abstractNote = {In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.},
doi = {10.1016/j.cma.2021.114296},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 389,
place = {United States},
year = {Sat Nov 27 00:00:00 EST 2021},
month = {Sat Nov 27 00:00:00 EST 2021}
}
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