A mathematical formalization of the parallel replica dynamics

Le Bris Claude (), Lelièvre Tony (), Luskin Mitchell () and Perez Danny ()
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Le Bris Claude: CERMICS, École des Ponts ParisTech, 6 & 8, avenue Blaise Pascal, 77455 Marne-La-Vallée; and INRIA Rocquencourt, MICMAC Project Team, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
Lelièvre Tony: CERMICS, École des Ponts ParisTech, 6 & 8, avenue Blaise Pascal, 77455 Marne-La-Vallée; and INRIA Rocquencourt, MICMAC Project Team, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay, France
Luskin Mitchell: School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN 55455, USA
Perez Danny: Theoretical Division T-1, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

Monte Carlo Methods and Applications, 2012, vol. 18, issue 2, 119-146

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.

Keywords: Parallel replica dynamics; quasi-stationary distribution; molecular dynamics (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1515/mcma-2012-0003

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