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Uncertainty quantification of sensitivities of time-average quantities in chaotic systems

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Title: Uncertainty quantification of sensitivities of time-average quantities in chaotic systems
Authors: Kantarakias, K
Shawki, K
Papadakis, G
Item Type: Journal Article
Abstract: We consider time-average quantities of chaotic systems and their sensitivity to system parameters. When the parameters are random variables with a prescribed probability density function, the sensitivities are also random. The central aim of the paper is to study and quantify the uncertainty of the sensitivities; this is useful to know in robust design applications. To this end, we couple the nonintrusive polynomial chaos expansion (PCE) with the multiple shooting shadowing (MSS) method, and apply the coupled method to two standard chaotic systems, the Lorenz system and the Kuramoto-Sivashinsky equation. The method leads to accurate results that match well with Monte Carlo simulations (even for low chaos orders, at least for the two systems examined), but it is costly. However, if we apply the concept of shadowing to the system trajectories evaluated at the quadrature integration points of PCE, then the resulting regularization can lead to significant computational savings. We call the new method shadowed PCE (sPCE).
Issue Date: 28-Feb-2020
Date of Acceptance: 10-Feb-2020
URI: http://hdl.handle.net/10044/1/77868
DOI: 10.1103/PhysRevE.101.022223
ISSN: 2470-0045
Publisher: American Physical Society
Journal / Book Title: Physical Review E
Volume: 101
Issue: 2
Copyright Statement: © 2020 American Physical Society
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Publication Status: Published
Article Number: 022223
Online Publication Date: 2020-02-28
Appears in Collections:Aeronautics