AUTHOR=Chertkov Andrei , Oseledets Ivan TITLE=Solution of the Fokker–Planck Equation by Cross Approximation Method in the Tensor Train Format JOURNAL=Frontiers in Artificial Intelligence VOLUME=4 YEAR=2021 URL=https://www.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2021.668215 DOI=10.3389/frai.2021.668215 ISSN=2624-8212 ABSTRACT=

We propose the novel numerical scheme for solution of the multidimensional Fokker–Planck equation, which is based on the Chebyshev interpolation and the spectral differentiation techniques as well as low rank tensor approximations, namely, the tensor train decomposition and the multidimensional cross approximation method, which in combination makes it possible to drastically reduce the number of degrees of freedom required to maintain accuracy as dimensionality increases. We demonstrate the effectiveness of the proposed approach on a number of multidimensional problems, including Ornstein-Uhlenbeck process and the dumbbell model. The developed computationally efficient solver can be used in a wide range of practically significant problems, including density estimation in machine learning applications.