In the study of stochastic dynamics, the committor function describes the probability that a process starting from an initial configuration $x$ will reach set $A$ before set $B$. This paper introduces a fast and interpretable method for approximating the committor, called the "fast committor machine" (FCM). The FCM is based on simulated trajectory data, and it uses this data to train a kernel model. The FCM identifies low-dimensional subspaces that optimally describe the $A$ to $B$ transitions, and the subspaces are emphasized in the kernel model. The FCM uses randomized numerical linear algebra to train the model with runtime that scales linearly in the number of data points. This paper applies the FCM to example systems including the alanine dipeptide miniprotein: in these experiments, the FCM is generally more accurate and trains more quickly than a neural network with a similar number of parameters.

翻译：在随机动力学研究中，通勤函数描述了从初始构型$x$出发的过程在到达集合$B$之前先到达集合$A$的概率。本文提出了一种快速且可解释的通勤函数近似方法，称为"快速通勤机"（FCM）。FCM基于模拟轨迹数据，利用这些数据训练核模型。该方法能够识别出最优描述$A$到$B$跃迁的低维子空间，并在核模型中强化这些子空间。FCM采用随机数值线性代数技术进行模型训练，其运行时间与数据点数量呈线性关系。本文将该方法应用于包括二丙氨酸小蛋白在内的示例系统：实验表明，在参数数量相近的情况下，FCM通常比神经网络具有更高的精度和更快的训练速度。