A high-order fractional physics-informed neural network (fPINN) for solving time fractional diffusion equations with Caputo derivatives

‎In this paper‎, ‎a high-order fractional physics-informed neural network (fPINN) for solving time fractional diffusion equations with Caputo derivatives is presented‎. ‎To design the scheme‎, ‎the Caputo temporal derivative is approximated using a high-order method‎, ‎named L1-2-3‎. ‎Then we use the physics-informed neural network (PINN) to employ automatic differentiation and minimize the cost function with respect to the neural network parameters‎. ‎We prove that the loss function converges to zero and illustrate the effectiveness of the method by providing numerical examples‎.