Ergodic sensitivity analysis of one-dimensional chaotic maps
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1-s2.0-S209503492030074X-main.pdf
Description
Published version
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2.23 MB
Format
Adobe PDF
Checksum (MD5)
ab366fcc2f82303b13247b6fd539a123
Author(s)
Śliwiak, Adam A
Chandramoorthy, Nisha
Wang, Qiqi
Date Issued
2020
Journal
Theoretical and Applied Mechanics Letters
Publisher
Elsevier BV
Version
Final published version
Abstract
© 2020 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic, chaotic systems, rigorously based on the theory of hyperbolic dynamics. We illustrate S3 on one-dimensional chaotic maps, revealing its computational advantage over naïve finite difference computations of the same statistical response. In addition, we provide an intuitive explanation of the key components of the S3 algorithm, including the density gradient function.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Center for Computational Science and Engineering
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.taml.2020.01.058
