Extreme event quantification in dynamical systems with random components

Giovanni Dematteis, Tobias Grafke, Eric Vanden-Eijnden

Research output: Contribution to journalArticle

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 Schr\"odinger equation with random initial conditions.

Original languageEnglish (US)
Pages (from-to)1029-1059
Number of pages31
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume7
Issue number3
DOIs
StatePublished - 2019

Keywords

  • extreme events
  • large deviation theory
  • nonlinear Schrodinger equation
  • optimal control
  • solitons

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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