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Title: Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations

Abstract

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis is made possible by explicit forms for the gradients of a cost function in terms of the susceptibility of driven trajectories to changes in variational parameters. We consider probabilities of time-integrated dynamical observables as characterized by their large deviation functions and find that in many cases, the variational estimate is quantitatively accurate. Additionally, we provide expressions to exactly correct the variational estimate that can be evaluated directly. We benchmark this algorithm against the numerically exact solution of a model of a driven particle in a periodic potential, where the control force can be represented with a complete basis. Additionally, we then demonstrate the utility of the algorithm in a model of repulsive particles on a line, which undergo a dynamical phase transition, resulting in singular changes to the form of the optimal control force. In both systems, we find fast convergence and are able to evaluate large deviation functions with significant increases in statistical efficiency over alternative Monte Carlo approaches.

Authors:
 [1]; ORCiD logo [2]
  1. Univ. of California, Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States); Kavli Energy NanoScience Institute, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES), Chemical Sciences, Geosciences & Biosciences Division; USDOE
OSTI Identifier:
1721632
Alternate Identifier(s):
OSTI ID: 1580664
Grant/Contract Number:  
AC02-05CH11231; SC0019375
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 24; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Probability theory; Monte Carlo methods; path integral formulation; molecular dynamics; many body systems; optimization algorithms; control theory; nonequilibrium statistical mechanics

Citation Formats

Das, Avishek, and Limmer, David T. Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations. United States: N. p., 2019. Web. doi:10.1063/1.5128956.
Das, Avishek, & Limmer, David T. Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations. United States. https://doi.org/10.1063/1.5128956
Das, Avishek, and Limmer, David T. Sat . "Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations". United States. https://doi.org/10.1063/1.5128956. https://www.osti.gov/servlets/purl/1721632.
@article{osti_1721632,
title = {Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations},
author = {Das, Avishek and Limmer, David T.},
abstractNote = {We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis is made possible by explicit forms for the gradients of a cost function in terms of the susceptibility of driven trajectories to changes in variational parameters. We consider probabilities of time-integrated dynamical observables as characterized by their large deviation functions and find that in many cases, the variational estimate is quantitatively accurate. Additionally, we provide expressions to exactly correct the variational estimate that can be evaluated directly. We benchmark this algorithm against the numerically exact solution of a model of a driven particle in a periodic potential, where the control force can be represented with a complete basis. Additionally, we then demonstrate the utility of the algorithm in a model of repulsive particles on a line, which undergo a dynamical phase transition, resulting in singular changes to the form of the optimal control force. In both systems, we find fast convergence and are able to evaluate large deviation functions with significant increases in statistical efficiency over alternative Monte Carlo approaches.},
doi = {10.1063/1.5128956},
journal = {Journal of Chemical Physics},
number = 24,
volume = 151,
place = {United States},
year = {Sat Dec 28 00:00:00 EST 2019},
month = {Sat Dec 28 00:00:00 EST 2019}
}

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Works referencing / citing this record:

Differentiable Molecular Simulations for Control and Learning
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