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Numerical computation of rare events via large deviation theory
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Grafke, Tobias and Vanden-Eijnden, Eric (2019) Numerical computation of rare events via large deviation theory. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (6). 063118 . doi:10.1063/1.5084025 ISSN 1054-1500.
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WRAP-Numerical-computation-rare-events-deviation-theory-Grafke-2019.pdf - Accepted Version - Requires a PDF viewer. Download (2370Kb) | Preview |
Official URL: https://doi.org/10.1063/1.5084025
Abstract
An overview of rare events 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 trade-offs. 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.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Large deviations, Algorithms | |||||||||
| Journal or Publication Title: | Chaos: An Interdisciplinary Journal of Nonlinear Science | |||||||||
| Publisher: | American Institute of Physics | |||||||||
| ISSN: | 1054-1500 | |||||||||
| Official Date: | 24 June 2019 | |||||||||
| Dates: |
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| Volume: | 29 | |||||||||
| Number: | 6 | |||||||||
| Article Number: | 063118 | |||||||||
| DOI: | 10.1063/1.5084025 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | The following article has been accepted by Chaos. After it is published, it will be found at https://aip.scitation.org/journal/cha | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 6 June 2019 | |||||||||
| Date of first compliant Open Access: | 10 June 2019 | |||||||||
| RIOXX Funder/Project Grant: |
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