A tensor decomposition approach to high dimensional stationary Fokker-Planck equations

This paper addresses the curse of dimensionality in the numerical solution of stationary Fokker-Planck equations. Combined with Chebyshev spectral differentiation, the tensor approach significantly reduces the degrees of freedom of the approximation essentially in exchange for nonlinearity, such that the resulting discretized nonlinear system is solved by alternating least squares. Enforcement of the normality condition via a penalty method avoids the need for exploration of the the null space of the discretized Fokker-Planck operator. The proposed method enables a drastic reduction of degrees of freedom required to maintain accuracy as dimensionality increases. Numerical results are presented to illustrate the effectiveness of the proposed method.