In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in some numerical experiments with low frequencies. Therein the new approach is compared to a classical domain decomposition method. Moreover, we highlight current challenges of training and testing with different wave numbers and we provide information on the behaviour of the neural-network, such as convergence of the loss function, and different activation functions.

翻译：本文研究时谐Maxwell方程组及其基于区域分解法的数值求解。创新性地提出一种前馈神经网络增强的子域界面条件逼近方法，其优势在于无需每次重新求解Maxwell系统即可更新界面条件。主要工作包括区域分解神经网络构建的详细描述及训练过程。为验证该概念证明，我们在低频数值实验中研究了若干子域情况，并将新方法与经典区域分解方法进行对比。此外，我们重点探讨了不同波数下训练与测试面临的挑战，并提供了神经网络行为的相关信息，例如损失函数收敛性及不同激活函数的影响。