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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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WRAP-extreme-event-quantification-dynamical-systems-random-Grafke-019.pdf - Accepted Version - Requires a PDF viewer. Download (1317Kb) | Preview |
Official URL: https://doi.org/10.1137/18M1211003
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 | |||||||||||||||
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| 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: |
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| 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: |
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