Supervised Learning and the Finite-Temperature String Method for Computing Committor Functions and Reaction Rates

The committor function, the probability that a system enters the product state before the reactant state, determines the reaction rates and transition pathways for a given rare-event problem. Recent work [1] constructed an algorithm where a neural network that represents the committor function is trained with data obtained from importance sampling. In this work [2], we extend their approach by combining it with supervised learning, where sample-mean estimates of the committor function obtained via short simulations are used to aid the training of the neural network, and the finite-temperature string (FTS) method, which enables homogeneous sampling across the transition pathway. We show that these modifications are crucial for obtaining accurate estimates of the committor function and reaction rates on systems with non-convex potential energy, where reference solutions are known. We also show that the sampling distribution of reaction rates estimated from algorithms employing the FTS method obeys a log-normal distribution, allowing accurate estimation of reaction rates with small sample size.

1. GM Rotskoff, AR Mitchell, E Vanden-Eijnden. arXiv:2008.06334

2. MR Hasyim, CH Batton, KK Mandadapu. arXiv:2107.13522