A mathematical formalization of the parallel replica dynamics

Claude Le Bris, Tony Lelièvre, Mitchell Luskin, Danny Perez

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

We propose a mathematical analysis of a well-known numerical approach used in molecular dynamics to efficiently sample a coarse-grained description of the original trajectory (in terms of state-to-state dynamics). This technique is called parallel replica dynamics and has been introduced by Arthur F. Voter. The principle is to introduce many replicas of the original dynamics, and to consider the first transition event observed among all the replicas. The effective physical time is obtained by summing up all the times elapsed for all replicas. Using a parallel implementation, a speed-up of the order of the number of replicas can thus be obtained, allowing longer time scales to be computed. By drawing connections with the theory of Markov processes and, in particular, exploiting the notion of quasi-stationary distribution, we provide a mathematical setting appropriate for assessing theoretically the performance of the approach, and possibly improving it.

Original languageEnglish (US)
Pages (from-to)119-146
Number of pages28
JournalMonte Carlo Methods and Applications
Volume18
Issue number2
DOIs
StatePublished - Jun 2012

Bibliographical note

Funding Information:
The second author acknowledgessupport from the Agence Nationale de la Recherche, under grant ANR-09-BLAN-0216-01 (MEGAS). The third and fourth authors acknowledgefunding by the US Department of Energy under award DE-FG02-09ER25880/DE-SC0002085. Work at Los Alamos National Laboratory (LANL) was funded by the Office of Science, Office of Advanced Scientific Computing Research. LANL is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. DOE under Contract No. DE-AC52-06NA25396.

Keywords

  • Molecular dynamics
  • Parallel replica dynamics
  • Quasi-stationary distribution

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