Solving parametric elliptic interface problems via interfaced operator network

Learning operator mapping between infinite-dimensional Banach spaces via neural networks has attracted a considerable amount of attention in recent years. In this work, we propose an interfaced operator network (IONet) to solve parametric elliptic interface PDEs, where different coefficients, source terms and boundary conditions are considered as input features. To capture the discontinuities of both input functions and output solutions across the interface, IONet divides the entire domain into several separate sub-domains according to the interface, and leverages multiple branch networks and truck networks. Each branch network extracts latent representations of input functions at a fixed number of sensors on a specific sub-domain, and each truck network is responsible for output solutions on one sub-domain. In addition, tailored physics-informed loss of IONet is proposed to ensure physical consistency, which greatly reduces the requirement for training datasets and makes IONet effective without any paired input-output observations in the interior of the computational domain. Extensive numerical studies show that IONet outperforms existing state-of-the-art deep operator networks in terms of accuracy, efficiency, and versatility.