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

TL;DR

This paper introduces a novel physics-informed neural network approach tailored for multi-material diffusion problems, effectively handling interface conditions and non-smooth functions, with verified robustness through numerical experiments.

Contribution

The paper proposes a new PINN method that incorporates interface conditions and specialized strategies to accurately solve multi-material diffusion equations, overcoming limitations of standard PINNs.

Findings

The method accurately predicts multi-material diffusion solutions.

It effectively handles non-smooth functions and interface conditions.

Numerical experiments confirm robustness and effectiveness.

Abstract

Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately solve the multi-material diffusion equation. The new method applies continuity conditions at the material interface derived from the property of the diffusion equation, and combines the distinctive spatial separation strategy and the loss term normalization strategy to solve the problem that the residual points cannot be arranged at the material interface, the problem that it is difficult to express non-smooth functions with a single neural network, and the problem that the neural network is difficult to optimize the loss function with different magnitudes of loss terms, which finally provides the available prediction function for a class of multi-material diffusion problems. Numerical experiments verify the robustness and effectiveness of the new method.