Improved diffusion monte carlo

Martin Hairer, Jonathan Weare

Research output: Contribution to journalArticle

Abstract

We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the "naïve" generalization of the standard algorithm would be impractical due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a Lennard-Jones cluster), as well as a high-frequency data assimilation problem.

Original languageEnglish (US)
Pages (from-to)1995-2021
Number of pages27
JournalCommunications on Pure and Applied Mathematics
Volume67
Issue number12
DOIs
StatePublished - Jan 1 2014

Fingerprint

Rare Event Simulation
High-frequency Data
Data Assimilation
Lennard-Jones
Monte Carlo Algorithm
Redistribution
Explosion
Workload
Explosions
Demonstrate
Standards
Simulation
Generalization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Improved diffusion monte carlo. / Hairer, Martin; Weare, Jonathan.

In: Communications on Pure and Applied Mathematics, Vol. 67, No. 12, 01.01.2014, p. 1995-2021.

Research output: Contribution to journalArticle

Hairer, Martin ; Weare, Jonathan. / Improved diffusion monte carlo. In: Communications on Pure and Applied Mathematics. 2014 ; Vol. 67, No. 12. pp. 1995-2021.
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