David Aristoff, Mats Johnson, Gideon Simpson, Robert J Webber
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引用次数: 0
摘要
在随机系统研究中,委顿函数描述了一个系统从初始配置 x 出发,在到达集合 A 之前到达集合 B 的概率。本文介绍了一种用于逼近委顿函数的高效且可解释的算法,称为 "快速委顿机"(FCM)。FCM 使用模拟轨迹数据来建立一个基于核的委顿器模型。构建核函数的目的是强调低维子空间,以最佳方式描述 A 到 B 的转换。核模型中的系数使用随机线性代数确定,因此运行时间与数据点数量成线性比例。在涉及三孔电位和丙氨酸二肽的数值实验中,FCM 比具有相同参数数的神经网络具有更高的准确性和更快的训练速度。与神经网络相比,FCM 的可解释性也更强。
The fast committor machine: Interpretable prediction with kernels.
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 with 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.
期刊介绍:
The Journal of Chemical Physics publishes quantitative and rigorous science of long-lasting value in methods and applications of chemical physics. The Journal also publishes brief Communications of significant new findings, Perspectives on the latest advances in the field, and Special Topic issues. The Journal focuses on innovative research in experimental and theoretical areas of chemical physics, including spectroscopy, dynamics, kinetics, statistical mechanics, and quantum mechanics. In addition, topical areas such as polymers, soft matter, materials, surfaces/interfaces, and systems of biological relevance are of increasing importance.
Topical coverage includes:
Theoretical Methods and Algorithms
Advanced Experimental Techniques
Atoms, Molecules, and Clusters
Liquids, Glasses, and Crystals
Surfaces, Interfaces, and Materials
Polymers and Soft Matter
Biological Molecules and Networks.