The fast committor machine: Interpretable prediction with kernels

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.