Physics Informed Neural Network Method For the Numerical Solution of Fractional Diffusion Equations

Artificial neural networks are increasingly used to construct continuous solution functions for solving various kinds of differential equations. In this study, we propose a physics informed neural network (PINN) method to solve fractional diffusion equations with variable coefficients on a finite domain. The PINN generate approximate solutions to the fractional PDE by training to minimize the physical loss function consisting of residual, boundary condition and initial condition parts. Fractional PDE is discretized with the Grunwald-Letnikov formula and the resulted semi-discrete equation is used to construct the residual function of the PINN. Numerical experiments show that the present PINN method provides accurate solutions on the considered computational space-time domain.