Point cloud discretization of Fokker-Planck operators for committor functions

TL;DR

This paper introduces a novel point cloud discretization method for Fokker-Planck operators to compute committor functions, assuming transitions occur on low-dimensional manifolds within high-dimensional spaces, validated by numerical examples.

Contribution

The work develops a new discretization approach for Fokker-Planck operators tailored for high-dimensional stochastic systems with low-dimensional transition manifolds.

Findings

Effective computation of committor functions demonstrated on model systems

Method leverages low-dimensional manifold structure for efficiency

Numerical validation confirms accuracy and applicability

Abstract

The committor functions provide useful information to the understanding of transitions of a stochastic system between disjoint regions in phase space. In this work, we develop a point cloud discretization for Fokker-Planck operators to numerically calculate the committor function, with the assumption that the transition occurs on an intrinsically low-dimensional manifold in the ambient potentially high dimensional configurational space of the stochastic system. Numerical examples on model systems validate the effectiveness of the proposed method.