Aristoff David, Johnson Mats, Simpson Gideon, Webber Robert J
Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA.
Mathematics, Drexel University, Philadelphia, Pennsylvania 19104, USA.
J Chem Phys. 2024 Aug 28;161(8). doi: 10.1063/5.0222798.
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.
在随机系统的研究中，反应坐标函数描述了一个从初始构型x开始的系统在到达集合A之前先到达集合B的概率。本文介绍了一种用于近似反应坐标函数的高效且可解释的算法，称为“快速反应坐标机”（FCM）。FCM使用模拟轨迹数据来构建基于核的反应坐标函数模型。核函数的构建旨在强调能最佳描述从A到B转变的低维子空间。核模型中的系数通过随机线性代数确定，从而使运行时间与数据点数量呈线性比例关系。在涉及三阱势和丙氨酸二肽的数值实验中，FCM比具有相同参数数量的神经网络具有更高的准确性且训练速度更快。FCM也比神经网络更具可解释性。
