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Numerical analysis of parallel replica dynamics

Published online by Cambridge University Press:  09 July 2013

Gideon Simpson  and
Mitchell Luskin
Gideon Simpson
Affiliation:
School of Mathematics, University of Minnesota, 206 Church St SE, 127 Vincent Hall, Minneapolis MN 55455, USA.. gsimpson@umn.edu; luskin@umn.edu
Mitchell Luskin
Affiliation:
School of Mathematics, University of Minnesota, 206 Church St SE, 127 Vincent Hall, Minneapolis MN 55455, USA.. gsimpson@umn.edu; luskin@umn.edu
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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.

Keywords

Accelerated dynamicsrare eventsparallel replica
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 5 , September 2013 , pp. 1287 - 1314
Copyright
© EDP Sciences, SMAI, 2013

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