Point cloud discretization of Fokker-Planck operators for committor functions
This work provides a numerical tool for computing committor functions in high-dimensional stochastic systems, which is important for understanding rare transitions in fields like chemistry and physics.
The authors developed a point cloud discretization method for Fokker-Planck operators to compute committor functions for stochastic systems on low-dimensional manifolds. Numerical examples on model systems validated the method's effectiveness.
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.