A Domain-adaptive Physics-informed Neural Network for Inverse Problems
  of Maxwell's Equations in Heterogeneous Media
Shiyuan Piao Hong Gu Aina Wang Pan Qin
Maxwell's equations are a collection of coupled partial differential
equations (PDEs) that, together with the Lorentz force law, constitute the
basis of classical electromagnetism and electric circuits. Effectively 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 PDEs. However, PINNs still
struggle to solve Maxwell's equations in heterogeneous media. To this end, we
propose a domain-adaptive PINN (da-PINN) to solve inverse problems of Maxwell's
equations in heterogeneous media. First, we propose a location parameter of
media interface to decompose the whole domain into several sub-domains.
Furthermore, the electromagnetic interface conditions are incorporated into a
loss function to improve the prediction performance near the interface. Then,
we propose a domain-adaptive training strategy for da-PINN. Finally, the
effectiveness of da-PINN is verified with two case studies.