Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

Khodabakhshi, Parisa; Willcox, Karen E.

doi:10.1016/j.cma.2021.114296

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

Journal Article · Sat Nov 27 00:00:00 EST 2021 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2021.114296· OSTI ID:1976972

Khodabakhshi, Parisa ^[1]; ^[2]

University of Texas, Austin, TX (United States); OSTI
University of Texas, Austin, TX (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: University of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0019303

OSTI ID:: 1976972

Alternate ID(s):: OSTI ID: 1840636

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 389; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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