TY - JOUR
T1 - Numerical computation of rare events via large deviation theory
AU - Grafke, Tobias
AU - Vanden-Eijnden, Eric
N1 - Funding Information:
We thank Freddy Bouchet, Grégoire Ferré, Robert Jack, and Jonathan Weare for useful discussions about genealogical algorithms. E.V.-E. is supported in part by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation (NSF) under Award No. DMR-1420073 and by the NSF under Award No. DMS-1522767.
Publisher Copyright:
© 2019 Author(s).
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
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U2 - 10.1063/1.5084025
DO - 10.1063/1.5084025
M3 - Article
C2 - 31266328
AN - SCOPUS:85068162844
VL - 29
JO - Chaos
JF - Chaos
SN - 1054-1500
IS - 6
M1 - 063118
ER -