The fast committor machine: Interpretable prediction with kernels

2024/05/16 by Aristoff, D., Johnson, M., Simpson, G. +1 · 2 citations
#65C30 #65C40 #82C31 #82C32 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2405.10410

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.

Cited by

• An exact multiple-time-step variational formulation for the committor and the transition rate
• Nonparametric Reaction Coordinate Optimization with Histories: A Framework for Rare Event Dynamics

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