Approximating committor functions: Objective functions and enhanced sampling

Many molecular dynamics simulations aim to study transitions between two states (from reactant to product states). In this context, the committor function (which gives, for a given molecular configuration, the probability of reaching the product state before the reactant state) is a pivotal quantity, in particular because it is the optimal importance function for rare-event simulation methods, such as importance sampling or splitting techniques. These methods are used to sample the reactive path ensemble and estimate, for example, the transition rate. However, learning such a function is generally a challenging task due to the high dimensionality of the configuration space. In this work, after reviewing existing methodologies to construct approximate committor functions, we propose a new loss function based on the application of Itō's formula to learn the committor function with a minimization procedure on the parameters of a neural network. After comparing this novel approach to existing procedures on the Müller-Brown potential, we introduce a coupling strategy with the Adaptive Multilevel Splitting method to better approximate the committor function by improving the sampling of the reactive trajectories. This methodology, in which the committor function is iteratively learned, initially requires only knowledge of the reactant and product states.