Numerical computation of rare events via large deviation theory

Tobias Grafke, Eric Vanden-Eijnden

Research output: Contribution to journalArticle

Abstract

An overview of rare event algorithms based on large deviation theory (LDT) is presented. It covers a range of numerical schemes to compute the large deviation minimizer in various setups and discusses best practices, common pitfalls, and implementation tradeoffs. Generalizations, extensions, and improvements of the minimum action methods are proposed. These algorithms are tested on example problems which illustrate several common difficulties which arise, e.g., when the forcing is degenerate or multiplicative, or the systems are infinite-dimensional. Generalizations to processes driven by non-Gaussian noises or random initial data and parameters are also discussed, along with the connection between the LDT-based approach reviewed here and other methods, such as stochastic field theory and optimal control. Finally, the integration of this approach in importance sampling methods using, e.g., genealogical algorithms, is explored.

Original languageEnglish (US)
Article number063118
JournalChaos
Volume29
Issue number6
DOIs
StatePublished - Jun 1 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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