Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems
Name
Constantine-2012-RESIDUAL MINIMIZING MODEL INTERPOLATION.pdf
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1.19 MB
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Adobe PDF
Checksum (MD5)
e21d9c49f5a073a4022b7db093c008ce
Author(s)
Constantine, Paul G.
Wang, Qiqi
Date Issued
July 2012
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Constantine, Paul G., and Qiqi Wang. “Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems.” SIAM Journal on Scientific Computing 34.4 (2012): A2118–A2144. © 2012, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. It is particularly appropriate when one wishes to approximate the states at a few points in time without time marching from the initial conditions. We prove some interesting characteristics of the scheme, including an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics---a three-state system with one parameter controlling the stiffness---and conductive heat transfer---a nonlinear parabolic PDE with a random field model for the thermal conductivity.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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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/10.1137/100816717
