Learning the committor probability using data-driven path collective variables

We have developed a new method aimed at predicting the committor probability for a system of two metastable states, focusing on a data-driven generalization of path collective variables. In this approach, we perform kernel ridge regression of the committor within a first projection of the Cartesian coordinates onto a subspace formed by collective variables (CVs). This subspace can be arbitrarily formed, e.g. by selecting a list of typical scalar CVs, or by using more abstract, high-dimensional CVs. The obtained collective variable is a one-dimensional estimatior of the committor, which makes for easy comparison of CV subspaces. This CV can subsequently be used for molecular dynamics or Monte Carlo simulations, with optional biasing. We apply this methodology to the well-known problem of ion pairing in water, with a focus on LiF, and show that better estimators of the committor can be obtained by taking into account information related to the solvent compared to the only interionic distance.