  We present a time dependent variational method to learn the mechanisms of
equilibrium reactive processes and efficiently evaluate their rates within a
transition path ensemble. This approach builds off variational path sampling
methodology by approximating the time dependent commitment probability within a
neural network ansatz. The reaction mechanisms inferred through this approach
are elucidated by a novel decomposition of the rate in terms of the components
of a stochastic path action conditioned on a transition. This decomposition
affords an ability to resolve the typical contribution of each reactive mode
and their couplings to the rare event. The associated rate evaluation is
variational and systematically improvable through the development of a cumulant
expansion. We demonstrate this method in both over- and under-damped stochastic
equations of motion, in low-dimensional model systems and the isomerization of
solvated alanine dipeptide. In all examples, we find that we can obtain
quantitatively accurate estimates of the rates of the reactive events with
minimal trajectory statistics, and gain unique insight into the transitions
through the analysis of their commitment probability.
