Variational deep learning of equilibrium transition path ensembles

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.

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Cited by in corpus (6)

• Perspective: How to overcome dynamical density functional theory
• Unveiling interatomic distances influencing the reaction coordinates in alanine dipeptide isomerization: An explainable deep learning approach
• Variational time reversal for free energy estimation in nonequilibrium steady states
• Investigating the hyperparameter space of deep neural network models for reaction coordinates
• Time-Asymmetric Fluctuation Theorem and Efficient Free Energy Estimation
• Deep learning of committor and explainable artificial intelligence analysis for identifying reaction coordinates