Numerical analysis of parallel replica dynamics

Gideon Simpson, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit distribution from a given well for a single process can be approximated by the distribution of the first exit of N independent identical processes, each run for only 1 / N-th the amount of time. While promising, this leads to a series of numerical analysis questions about the accuracy of the exit distributions. Building upon the recent work in [C. Le Bris, T. Lelièvre, M. Luskin and D. Perez, Monte Carlo Methods Appl. 18 (2012) 119-146], we prove a unified error estimate on the exit distributions of the algorithm against an unaccelerated process. Furthermore, we study a dephasing mechanism, and prove that it will successfully complete.

Original languageEnglish (US)
Pages (from-to)1287-1314
Number of pages28
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume47
Issue number5
DOIs
StatePublished - Sep 2013

Keywords

  • Accelerated dynamics
  • Parallel replica
  • Rare events

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