Data-driven path collective variables
Arthur France-Lanord Hadrien Vroylandt Mathieu Salanne Benjamin Rotenberg A. Marco Saitta Fabio Pietrucci
Identifying optimal collective variables to model transformations, using
atomic-scale simulations, is a long-standing challenge. We propose a new method
for the generation, optimization, and comparison of collective variables, which
can be thought of as a data-driven generalization of the path collective
variable concept. It consists in a kernel ridge regression of the committor
probability, which encodes a transformation's progress. The resulting
collective variable is one-dimensional, interpretable, and differentiable,
making it appropriate for enhanced sampling simulations requiring biasing. We
demonstrate the validity of the method on two different applications: a
precipitation model, and the association of Li$^+$ and F$^-$ in water. For the
former, we show that global descriptors such as the permutation invariant
vector allow to reach an accuracy far from the one achieved \textit{via}
simpler, more intuitive variables. For the latter, we show that information
correlated with the transformation mechanism is contained in the first
solvation shell only, and that inertial effects prevent the derivation of
optimal collective variables from the atomic positions only.