Numerical analysis of parallel replica dynamics
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 5, p. 1287-1314

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.

DOI : https://doi.org/10.1051/m2an/2013068
Classification:  60H35,  65C20,  65C30,  70K70,  74S60
Keywords: accelerated dynamics, rare events, parallel replica
@article{M2AN_2013__47_5_1287_0,
     author = {Simpson, Gideon and Luskin, Mitchell},
     title = {Numerical analysis of parallel replica dynamics},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {5},
     year = {2013},
     pages = {1287-1314},
     doi = {10.1051/m2an/2013068},
     zbl = {1298.65016},
     mrnumber = {3100764},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2013__47_5_1287_0}
}
Simpson, Gideon; Luskin, Mitchell. Numerical analysis of parallel replica dynamics. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 5, pp. 1287-1314. doi : 10.1051/m2an/2013068. http://www.numdam.org/item/M2AN_2013__47_5_1287_0/

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