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Gaussian approximations for transition paths in molecular dynamics

Lu, Yulong and Stuart, Andrew M. and Weber, Hendrik (2016) Gaussian approximations for transition paths in molecular dynamics. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20161220-182307792

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Abstract

This paper is concerned with transition paths within the framework of the overdamped Langevin dynamics model of chemical reactions. We aim to give an efficient description of typical transition paths in the small temperature regime. We adopt a variational point of view and seek the best Gaussian approximation, with respect to Kullback-Leibler divergence, of the non-Gaussian distribution of the diffusion process. We interpret the mean of this Gaussian approximation as the "most likely path" and the covariance operator as a means to capture the typical fluctuations around this most likely path. We give an explicit expression for the Kullback-Leibler divergence in terms of the mean and the covariance operator for a natural class of Gaussian approximations and show the existence of minimisers for the variational problem. Then the low temperature limit is studied via Γ-convergence of the associated variational problem. The limiting functional consists of two parts: The first part only depends on the mean and coincides with the Γ-limit of the Freidlin-Wentzell rate functional. The second part depends on both, the mean and the covariance operator and is minimized if the dynamics are given by a time-inhomogenous Ornstein-Uhlenbeck process found by linearization of the Langevin dynamics around the Freidlin-Wentzell minimizer.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1604.06594arXivDiscussion Paper
Additional Information:The authors are grateful Frank Pinski for helpful discussions and insights. YL is is supported by EPSRC as part of the MASDOC DTC at the University of Warwick with grant No. EP/HO23364/1. The work of AMS is supported by DARPA, EPSRC and ONR. The work of HW is supported by EPSRC and the Royal Society.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/HO23364/1
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Royal SocietyUNSPECIFIED
Subject Keywords:Transition path, Kullback-Leibler approximation, Onsager-Machlup functional, large deviations, Gamma-convergence
Classification Code:MSC 2010: 28C20, 60G15, 60F10
Record Number:CaltechAUTHORS:20161220-182307792
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161220-182307792
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73040
Collection:CaltechAUTHORS
Deposited By: Linda Taddeo
Deposited On:21 Dec 2016 18:33
Last Modified:03 Oct 2019 16:24

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