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Characterization of Rare Events in Molecular Dynamics
Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
Konrad-Zuse Zentrum, Takustraße 7, 14195 Berlin, Germany
* Author to whom correspondence should be addressed.
Received: 13 September 2013; in revised form: 8 October 2013 / Accepted: 22 November 2013 / Published: 30 December 2013
Abstract: A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski’s equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods.
Keywords: rare events; molecular dynamics; optimal pathways; stochastic control; dynamic programming; change of measure; cumulant generating function
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Hartmann, C.; Banisch, R.; Sarich, M.; Badowski, T.; Schütte, C. Characterization of Rare Events in Molecular Dynamics. Entropy 2014, 16, 350-376.
Hartmann C, Banisch R, Sarich M, Badowski T, Schütte C. Characterization of Rare Events in Molecular Dynamics. Entropy. 2014; 16(1):350-376.
Hartmann, Carsten; Banisch, Ralf; Sarich, Marco; Badowski, Tomasz; Schütte, Christof. 2014. "Characterization of Rare Events in Molecular Dynamics." Entropy 16, no. 1: 350-376.