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We introduce a variational algorithm to estimate the likelihood of a rareevent within a nonequilibrium molecular dynamics simulation through theevaluation of an optimal control force. Optimization of a control force withina chosen basis is made possible by explicit forms for the gradients of a costfunction in terms of the susceptibility of driven trajectories to changes invariational parameters. We consider probabilities of time-integrated dynamicalobservables as characterized by their large deviation functions, and find thatin many cases the variational estimate is quantitatively accurate.Additionally, we provide expressions to exactly correct the variationalestimate that can be evaluated directly. We benchmark this algorithm againstthe numerically exact solution of a model of a driven particle in a periodicpotential, where the control force can be represented with a complete basis. Wethen demonstrate the utility of the algorithm in a model of repulsive particleson a line, which undergo a dynamical phase transition, resulting in singularchanges to the form of the optimal control force. In both systems, we find fastconvergence and are able to evaluate large deviation functions with significantincreases in statistical efficiency over alternative Monte Carlo approaches.

Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations