The fast committor machine: Interpretable prediction with kernels

Autor:	Aristoff, D., Johnson, M., Simpson, G., Webber, R. J.
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Computer Science - Machine Learning Statistics - Machine Learning 82C31 82C32 65C30 65C40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 10 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.10410 Zobrazit plný text záznamu View this record from Arxiv