Relative Entropy Methods for Calculating Committors

Motivated by challenges arising in molecular simulation, we analyze and develop methods of computing reactive trajectories and committor functions for systems described by the overdamped Langevin dynamics. Our main technical advance is a new loss function that measures the accuracy of approximations to the committor function related to a given chemical reaction or other rare transition event. Our loss admits a simple interpretation in terms of the distribution of reactive trajectories, and it can be computed in practice to compare the accuracies of different approximations of the committor. We also derive a method of calculating committors by direct minimization of the loss via stochastic gradient descent.