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

TL;DR

This paper introduces a domain-adaptive physics-informed neural network (da-PINN) that effectively solves inverse Maxwell's equations in heterogeneous media by incorporating interface conditions and a specialized training strategy.

Contribution

The paper presents a novel domain-adaptive PINN framework with interface handling and a new training strategy for Maxwell's equations in complex media.

Findings

da-PINN accurately models electromagnetic fields in heterogeneous media.

Incorporating interface conditions improves prediction accuracy near media boundaries.

The method is validated with two case studies demonstrating its effectiveness.

Abstract

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.