  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.
