Least Squares Shadowing Method for Sensitivity Analysis of Differential Equations
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15m1039067.pdf
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817.83 KB
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e7da699674185692b1aeb218a0b4c9fd
Author(s)
Chater, Mario
Ni, Angxiu
Blonigan, Patrick Joseph
Wang, Qiqi
Date Issued
November 2017
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Chater, Mario et al. “Least Squares Shadowing Method for Sensitivity Analysis of Differential Equations.” SIAM Journal on Numerical Analysis 55, 6 (January 2017): 3030–3046 © 2017 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
For a parameterized hyperbolic system du dt = f(u; s) the derivative of the ergodic average hJi = limT→∞ 1 T R T 0 J(u(t); s) to the parameter s can be computed via the least squares shadowing (LSS) algorithm. We assume that the system is ergodic, which means that hJi depends only on s (not on the initial condition of the hyperbolic system). The algorithm solves a constrained least squares problem and, from the solution to this problem, computes the desired derivative dhJi ds . The purpose of this paper is to prove that the value given by the LSS algorithm approaches the exact derivative when the timespan used to formulate the least squares problem grows to infinity. It then illustrates the convergence result through a numerical example.
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.
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DOI of Published Version
https://doi.org/10.1137/15M1039067
