Numerical solution of high dimensional stationary FokkerPlanck equations via tensor decomposition and Chebyshev spectral differentiation
This paper focuses on the curse of dimensionality in the numerical solution of the stationary FokkerPlanck equation for systems with state-independent excitation. A tensor decomposition approach is combined with Chebyshev spectral differentiation to drastically reduce the number of degrees of freedom required to maintain accuracy as dimensionality increases. Following the enforcement of the normality condition via a penalty method, the discretized system is solved using alternating least squares algorithm. Numerical results for a variety of systems, including separable/non-separable systems, linear/nonlinear systems and systems with/without closed-form stationary solutions up to ten dimensional state-space are presented to illustrate the effectiveness of the proposed method.
fokkerplanck equation tensor decomposition curse of dimensionality numerical partial differential equation chebyshev spectral method separation of variables