# Variational deep learning of equilibrium transition path ensembles

## TL;DR

This paper introduces a neural network-based variational method to analyze equilibrium transition paths, accurately estimate reaction rates, and elucidate mechanisms with minimal data in stochastic systems.

## Contribution

It develops a novel variational approach that combines neural networks and path sampling to efficiently learn reaction mechanisms and rate contributions in equilibrium processes.

## Key findings

- Accurately estimates reaction rates with minimal trajectories.
- Provides detailed insight into reactive mode contributions.
- Demonstrates effectiveness on model systems and alanine dipeptide.

## Abstract

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.