TY - JOUR

T1 - A mathematical formalization of the parallel replica dynamics

AU - Le Bris, Claude

AU - Lelièvre, Tony

AU - Luskin, Mitchell

AU - Perez, Danny

PY - 2012/6/1

Y1 - 2012/6/1

N2 - 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.

AB - 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.

KW - Molecular dynamics

KW - Parallel replica dynamics

KW - Quasi-stationary distribution

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U2 - 10.1515/mcma-2012-0003

DO - 10.1515/mcma-2012-0003

M3 - Article

AN - SCOPUS:84870270041

VL - 18

SP - 119

EP - 146

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 2

ER -