  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.
