Data-driven operator inference for nonintrusive projection-based model reduction
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Non-intrusive-model-reduction-Peherstorfer-Willcox.pdf
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Author(s)
Peherstorfer, Benjamin
Willcox, Karen E
Date Issued
April 2016
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Citation
Peherstorfer, Benjamin, and Karen Willcox. “Data-Driven Operator Inference for Nonintrusive Projection-Based Model Reduction.” Computer Methods in Applied Mechanics and Engineering 306 (July 2016): 196–215 © 2016 Elsevier B.V.
Version
Author's final manuscript
Abstract
This work presents a nonintrusive projection-based model reduction approach for full models based on time-dependent partial differential equations. Projection-based model reduction constructs the operators of a reduced model by projecting the equations of the full model onto a reduced space. Traditionally, this projection is intrusive, which means that the full-model operators are required either explicitly in an assembled form or implicitly through a routine that returns the action of the operators on a given vector; however, in many situations the full model is given as a black box that computes trajectories of the full-model states and outputs for given initial conditions and inputs, but does not provide the full-model operators. Our nonintrusive operator inference approach infers approximations of the reduced operators from the initial conditions, inputs, trajectories of the states, and outputs of the full model, without requiring the full-model operators. Our operator inference is applicable to full models that are linear in the state or have a low-order polynomial nonlinear term. The inferred operators are the solution of a least-squares problem and converge, with sufficient state trajectory data, in the Frobenius norm to the reduced operators that would be obtained via an intrusive projection of the full-model operators. Our numerical results demonstrate operator inference on a linear climate model and on a tubular reactor model with a polynomial nonlinear term of third order. Keywords: Nonintrusive model reduction; Data-driven model reduction; Black-box full model; Inference
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.CMA.2016.03.025
