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.

翻译：鉴于多材料扩散问题的广泛性以及标准PINN（物理信息神经网络）方法对此类问题的局限性，本文提出了一种能够精确求解多材料扩散方程的新型PINN方法。该方法利用扩散方程的特性，在材料界面处应用连续性条件，并结合独特的空间分离策略与损失项归一化策略，解决了残差点无法布置于材料界面、单一神经网络难以表达非光滑函数以及神经网络难以优化不同量级损失项的损失函数等问题，最终为一类多材料扩散问题提供了可用的预测函数。数值实验验证了该方法的鲁棒性与有效性。