A Domain-Adaptive Physics-Informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Media

Solving Maxwell's equations is crucial in various fields, like electromagnetic scattering and antenna design optimization. Physics-informed neural networks (PINNs) have shown powerful ability in solving partial differential equations. However, PINNs still struggle to solve Maxwell's equations in heterogeneous media due to a lack of knowledge of interface location and its physical attribution. To this end, we propose a domain-adaptive PINN (Da-PINN). First, we propose a parameter of media interface location to decompose the whole domain into several subdomains with homogeneous media. Furthermore, the parameter of interface location and the electromagnetic interface conditions are incorporated into the loss function. Then, we propose a domain-adaptive training strategy for adaptively decomposing the domain and optimizing Da-PINN. Finally, the effectiveness of Da-PINN is verified with two case studies. The method can be used to solve problems in heterogeneous media with a lack of knowledge of interface location and its physical attribution.