Trajectory stratification of stochastic dynamics

Aaron R. Dinner, Jonathan C. Mattingly, Jeremy O.B. Tempkin, Brian Van Koten, Jonathan Weare

Research output: Contribution to journalArticle

Abstract

We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of state space (strata), computing averages over the distributions of the trajectory fragments within the strata with minimal communication between them, and combining those averages with appropriate weights to yield averages with respect to the original underlying process. Our framework reveals the full generality and flexibility of trajectory stratification, and it illuminates a common mathematical structure shared by existing algorithms for sampling rare events. We demonstrate the power of the framework by defining strata in terms of both points in time and path-dependent variables for efficiently estimating averages that were not previously tractable.

Original languageEnglish (US)
Pages (from-to)909-938
Number of pages30
JournalSIAM Review
Volume60
Issue number4
DOIs
StatePublished - 2018

Keywords

  • Computational statistical mechanics
  • Molecular dynamics
  • Monte Carlo methods
  • Rare events

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics

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  • Cite this

    Dinner, A. R., Mattingly, J. C., Tempkin, J. O. B., Van Koten, B., & Weare, J. (2018). Trajectory stratification of stochastic dynamics. SIAM Review, 60(4), 909-938. https://doi.org/10.1137/16M1104329