Characterization of Rare Events in Molecular Dynamics

Please always quote using this URN: urn:nbn:de:0297-zib-42410
  • 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.

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Author:Carsten Hartmann, Ralf Banisch, Marco Sarich, Thomas Badowski, Christof Schütte
Document Type:ZIB-Report
Tag:change of measure; cumulant generating function; dynamic programming; moleculare dynamics; optimal pathways; rare events; stochastic control
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M20 Methods of relaxation type
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J45 Probabilistic potential theory [See also 31Cxx, 31D05]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Exx Stochastic systems and control / 93E20 Optimal stochastic control
Date of first Publication:2013/09/11
Series (Serial Number):ZIB-Report (13-51)
Published in:Appeared in Entropy (Special Issue), 16 (1)

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