A Domain-adaptive Physics-informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Media
This work addresses a specific bottleneck in computational electromagnetism for applications like electromagnetic scattering and antenna design, representing an incremental improvement over existing PINN methods.
The paper tackled the challenge of solving inverse problems for Maxwell's equations in heterogeneous media using physics-informed neural networks (PINNs), which struggle in such scenarios, and proposed a domain-adaptive PINN (da-PINN) that improved prediction performance near interfaces, as verified through two case studies.
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.