Variational Computation of the Committor for Reactive Events In and Out of Equilibrium

The identification of the committor, a function that encodes the exact reaction coordinate of rare events is a quintessential many-body problem in chemical and statistical physics. Of particular interest are out-of-equilibrium reactive processes, where the evaluation of the committor becomes intractable by a majority of current methods that rely on detailed balance. We present a method that employs a neural network ansatz with a variational optimization scheme to compute the exact committor function from a reactive trajectory ensemble. This function is related to the solution of the backward Kolmogorov equation and offers an optimal control policy to generate new uncorrelated reactive trajectories. Furthermore, we illustrate how this approach provides a novel way to decompose the rate and quantify the contributions to it from different degrees of freedom. We apply these methods to a variety of complex systems in and out of equilibrium including systems with active brownian particles and the isomerization of a peptide in solvent. Our results provide mechanistic insight into reactive events and address fundamental questions in kinetics regarding the choice of order parameters in molecular systems, and coupling of the rate to external driving.