  Learning operators mapping between infinite-dimensional Banach spaces via
neural networks has attracted a considerable amount of attention in recent
years. In this paper, 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 in both the input functions and the output solutions across the
interface, IONet divides the entire domain into several separate subdomains
according to the interface and uses multiple branch nets and trunk nets. Each
branch net extracts latent representations of input functions at a fixed number
of sensors on a specific subdomain, and each trunk net is responsible for
output solutions on one subdomain. Additionally, tailored physics-informed loss
of IONet is proposed to ensure physical consistency, which greatly reduces the
training dataset requirement and makes IONet effective without any paired
input-output observations inside the computational domain. Extensive numerical
studies demonstrate that IONet outperforms existing state-of-the-art deep
operator networks in terms of accuracy and versatility.
