Variational deep learning of equilibrium transition path ensembles

Kavli Affiliate: David T. Limmer

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| Summary:

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 of the 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.

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