A deep learning method for multi-material diffusion problems based on physics-informed neural networks

Abstract

Since the solutions of the multi-material diffusion problems are not smooth, the general physics-informed neural network (PINN) method does not work well for this problem. In this paper, we first give the interface continuity conditions which are necessarily added to the loss function as a loss term. Then, to adapt PINN for solving the multi-material diffusion problems with a single neural network, we propose a domain separation strategy. Furthermore, a normalization strategy for the loss terms is proposed to improve the prediction accuracy of the trained network. By combining the above techniques, we present the improved PINN methods called DS-PINN and nDS-PINN which are novel and advance the application of PINN for non-smooth solutions. Numerical experiments verify the robustness and accuracy of the new methods. Moreover, the new methods also perform well for the interface problems with jump conditions.