The committor functions provide useful information to the understanding of transitions of a stochastic system between disjoint regions in phase space. The committor functions are solutions to Dirichlet problems for Fokker-Planck operators in the high-dimensional phase space, and hence brings challenges to numerical methods. In this talk, we discuss some recent developments in numerical methods of solving for committor functions utilizing point cloud discretization and neural network ansatz. Based on joint works with Rongjie Lai, Yuehaw Khoo and Lexing Ying.
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