Time difference physics-informed neural network for fractional water wave models

Abstract

In this article, the time difference physics-informed neural network (TD-PINN) is considered to approximate the solution of fractional water wave models. Based on the TD-PINN framework, the spatial partial derivatives are approximated by applying the neural network’s automatic differential operation and the time direction is discretized by making use of the BDF2 with the L1 formula for the Caputo fractional derivative. We provide the detailed algorithm process based on our models. Finally, by choosing two different types of examples, we carry out numerical experiments to verify the effectiveness and feasibility of the proposed TD-PINN.