The fast committor machine: Interpretable prediction with kernels

TL;DR

The paper presents the fast committor machine, an efficient, interpretable kernel-based algorithm for approximating the committor function in stochastic systems, outperforming neural networks in accuracy and speed.

Contribution

Introduces the fast committor machine, a novel kernel-based method that efficiently approximates the committor function with enhanced interpretability and scalability.

Findings

Higher accuracy than neural networks with same parameters

Faster training due to linear scaling in data points

More interpretable model than neural networks

Abstract

In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration $x$ will reach a set $B$ before a set $A$. This paper introduces an efficient and interpretable algorithm for approximating the committor, called the "fast committor machine" (FCM). The FCM uses simulated trajectory data to build a kernel-based model of the committor. The kernel function is constructed to emphasize low-dimensional subspaces that optimally describe the $A$ to $B$ transitions. The coefficients in the kernel model are determined using randomized linear algebra, leading to a runtime that scales linearly in the number of data points. In numerical experiments involving a triple-well potential and alanine dipeptide, the FCM yields higher accuracy and trains more quickly than a neural network with the same number of parameters. The FCM is also more interpretable than the neural net.