Relative Entropy Methods for the Approximation of Reactive Trajectories
Motivated by challenges arising in molecular simulation, we study reactive trajectories of the overdamped Langevin dynamics, i.e. trajectories observed as they pass from a set A corresponding to the reagents of a chemical reaction to a set B corresponding to the products. Reactive trajectories are known to have the same distribution as trajectories of the overdamped Langevin dynamics biased by a singular drift related to the committor function. In this work, we assess the effect of replacing the exact singular drift with an approximation based on an approximate committor function. We derive a convenient formula for the relative entropy between the distributions of exact and approximate reactive trajectories, and we propose a stochastic gradient descent method for minimizing the entropy to train an approximate committor function on the fly while computing reactive trajectories. We also devise a model assessment procedure for comparing the qualities of different approximations to the committor function based on the relative entropy.