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.

我们提出了一种域自适应 PINN（da-PINN）来解决 Maxwell 方程在异质介质中的逆问题，并通过两个案例研究验证了 da-PINN 的有效性。