# Nonparametric Determination of the Committor in Multimolecular Systems

## TL;DR

This paper introduces a nonparametric method to determine the committor, a key variable in modeling molecular dynamics, using permutation-invariant collective variables.

## Contribution

The novel contribution is a systematic nonparametric approach to determine the committor for multimolecular systems with anisotropic interactions.

## Key findings

- The committor was effectively determined using permutationally invariant collective variables.
- The diffusive model along the committor matched kinetic properties from original dynamics.
- The method is general and applicable to machine learning approaches for longitudinal data.

## Abstract

A fundamental problem
in analyzing large longitudinal data sets
modeling dynamics in multimolecular systems is determining the underlying
free-energy landscapes as a function of the committor, the optimal
reaction coordinate. Here, we demonstrate that by combining a nonparametric
approach with a systematic method for generating permutationally invariant
collective variables, the committor can be effectively determined
to describe multimolecular aggregation in a system with anisotropic
interactions. The optimality of the committor is verified by a stringent
validation test, and it is shown that the diffusive model along the
committor yields kinetic properties identical to those derived from
the original dynamics. Our method is general and relevant to the large
machine learning community developing methods to determine the committor
from longitudinal data sets.