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.

翻译：麦克斯韦方程是一组耦合偏微分方程，与洛伦兹力定律共同构成经典电磁学和电路的基础。有效求解麦克斯韦方程在电磁散射和天线设计优化等各个领域至关重要。物理信息神经网络在求解偏微分方程方面展现出强大能力。然而，物理信息神经网络在求解异质介质中的麦克斯韦方程时仍面临困难。为此，我们提出了一种域自适应物理信息神经网络（da-PINN）来解决异质介质中麦克斯韦方程的逆问题。首先，我们提出了一个介质界面位置参数，将整个域分解为若干子域。此外，将电磁界面条件纳入损失函数，以提升界面附近的预测性能。然后，我们提出了一种针对da-PINN的域自适应训练策略。最后，通过两个案例验证了da-PINN的有效性。