Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates
Name
Peherstorfer-2015-Online adaptive reduction.pdf
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1.69 MB
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Adobe PDF
Checksum (MD5)
0e527ae9b5bbd941acb63fa03b966904
Author(s)
Peherstorfer, Benjamin
Willcox, Karen E.
Date Issued
August 2015
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Peherstorfer, Benjamin, and Karen Willcox. “Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates.” SIAM Journal on Scientific Computing 37, no. 4 (January 2015): A2123–A2150. © 2015, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
This work presents a nonlinear model reduction approach for systems of equations stemming from the discretization of partial differential equations with nonlinear terms. Our approach constructs a reduced system with proper orthogonal decomposition and the discrete empirical interpolation method (DEIM); however, whereas classical DEIM derives a linear approximation of the nonlinear terms in a static DEIM space generated in an offline phase, our method adapts the DEIM space as the online calculation proceeds and thus provides a nonlinear approximation. The online adaptation uses new data to produce a reduced system that accurately approximates behavior not anticipated in the offline phase. These online data are obtained by querying the full-order system during the online phase, but only at a few selected components to guarantee a computationally efficient adaptation. Compared to the classical static approach, our online adaptive and nonlinear model reduction approach achieves accuracy improvements of up to three orders of magnitude in our numerical experiments with time-dependent and steady-state nonlinear problems. The examples also demonstrate that through adaptivity, our reduced systems provide valid approximations of the full-order systems outside of the parameter domains for which they were initially built in the offline phase.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/140989169
