Solving for high-dimensional committor functions using artificial neural networks

  • Yuehaw KhooEmail author
  • Jianfeng Lu
  • Lexing Ying


In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of transition path theory, which satisfies a high-dimensional Fokker–Planck equation. By working with the variational formulation of such partial differential equation and parameterizing the committor function in terms of a neural network, approximations can be obtained via optimizing the neural network weights using stochastic algorithms. The numerical examples show that moderate accuracy can be achieved for high-dimensional problems.


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© SpringerNature 2018

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of Mathematics, Department of Chemistry and Department of PhysicsDuke UniversityDurhamUSA
  3. 3.Department of Mathematics and ICMEStanford UniversityStanfordUSA

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