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Extreme event quantification in dynamical systems with random components

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Dematteis, Giovanni, Grafke, Tobias and Vanden-Eijnden, Eric (2019) Extreme event quantification in dynamical systems with random components. SIAM/ASA Journal on Uncertainty Quantification, 7 (3). pp. 1029-1059. doi:10.1137/18M1211003

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Official URL: https://doi.org/10.1137/18M1211003

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Abstract

A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by making the unknown model parameters random with given statistics. Here this approach is used in concert with tools from large deviation theory (LDT) and optimal control to estimate the probability that some observables in a dynamical system go above a large threshold after some time, given the prior statistical information about the system’s parameters and/or its initial conditions. Specifically, it is established under which conditions such extreme events occur in a predictable way, as the minimizer of the LDT action functional. It is also shown how this minimization can be numerically performed in an efficient way using tools from optimal control. These findings are illustrated on the examples of a rod with random elasticity pulled by a time-dependent force, and the nonlinear Schrödinger equation (NLSE) with random initial conditions.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Large deviations, Schrödinger equation
Journal or Publication Title: SIAM/ASA Journal on Uncertainty Quantification
Publisher: SIAM
ISSN: 2166-2525
Official Date: 13 August 2019
Dates:
DateEvent
13 August 2019Published
20 May 2019Accepted
Volume: 7
Number: 3
Page Range: pp. 1029-1059
DOI: 10.1137/18M1211003
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: “First Published in SIAM/ASA Journal on Uncertainty Quantification in [volume and number, or year], published by the Society for Industrial and Applied Mathematics (SIAM)” and the copyright notice as stated in the article itself (e.g., “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”)
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © 2019, Society for Industrial and Applied Mathematics
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIEDPolitecnico di Torinohttp://dx.doi.org/10.13039/100013000
Dipartimenti di Eccellenza 2018-2022Ministero dell’Istruzione, dell’Università e della Ricercahttp://dx.doi.org/10.13039/501100003407
DMR-1420073 National Science Foundationhttp://dx.doi.org/10.13039/100000001
DMS-1522767National Science Foundationhttp://dx.doi.org/10.13039/100000001
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