The fast committor machine: Interpretable prediction with kernels
This work addresses the need for interpretable and efficient prediction of transition probabilities in stochastic systems, such as molecular dynamics, with incremental improvements over existing methods.
This paper tackles the problem of efficiently approximating the committor function in stochastic systems by introducing the fast committor machine (FCM), which uses kernel-based modeling and randomized linear algebra to achieve higher accuracy and faster training than a neural network with the same parameters in numerical experiments on a triple-well potential and alanine dipeptide.
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.