Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations

2019/09/30 by Avishek Das, David T. Limmer · 37 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Benchmark (surveying) #Convergence (economics) #Function (biology) #Markov Chains and Monte Carlo Methods #Monte Carlo method #Non-equilibrium thermodynamics #Observable #Optimal control #Sampling (signal processing) #Variational method #cond-mat.stat-mech #physics.chem-ph #stochastic dynamics and bifurcation

paper · pdf · doi:10.1063/1.5128956

published in The Journal of Chemical Physics 151(24), 244123 (American Institute of Physics) · 14 pages, 10 figures

openalex publication_date 2019/12/28 · openalex created_date 2020/01/10 · arxiv created 2021/01/12 · arxiv updated 2021/01/14 · openalex updated_date 2026/08/05

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. 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.

Citations

• Rayleigh-Ritz Calculation of Effective Potential Far from Equilibrium
• Dominant reaction pathways in high-dimensional systems
• Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems
• Dynamic transition in an atomic glass former: A molecular-dynamics evidence
• TRANSITIONPATHSAMPLING: Throwing Ropes Over Rough Mountain Passes, in the Dark
• Stochastic thermodynamics, fluctuation theorems and molecular machines
• Asymptotics for the wiener sausage
• Space–time thermodynamics of the glass transition
• Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time
• Nonlinear transport coefficients from large deviation functions

Cited by

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• Learning nonequilibrium control forces to characterize dynamical phase transitions