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

arXiv: https://arxiv.org/abs/2308.06436 · HTML: https://mlsanity.com/paper/2308.06436/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 12 Aug 2023.

## Builds on (most cited first, 7 of 7)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [Neural Inverse Operators for Solving PDE Inverse Problems](https://mlsanity.com/paper/2301.11167/) (2023)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Physics-informed neural networks for solving forward and inverse problems in complex beam systems](https://mlsanity.com/paper/2303.01055/) (2023)
- [Physics-informed machine learning for moving load problems](https://mlsanity.com/paper/2304.00369/) (2023)

## Built on by (most cited first, 7 of 7)

- [Accurate and scalable deep Maxwell solvers using multilevel iterative methods](https://mlsanity.com/paper/2509.03622/) (2025)
- [Ambient Physics: Training Neural PDE Solvers with Partial Observations](https://mlsanity.com/paper/2602.13873/) (2026)
- [Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappings](https://mlsanity.com/paper/2602.16193/) (2026)
- [Generalizing Deep Surrogate Solvers for Broadband Electromagnetic Field Prediction at Unseen Wavelengths](https://mlsanity.com/paper/2408.02971/) (2024)
- [GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media](https://mlsanity.com/paper/2602.14642/) (2026)
- [Virtual boundary integral neural network for three-dimensional exterior acoustic problems](https://mlsanity.com/paper/2604.18636/) (2026)
- [Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data](https://mlsanity.com/paper/2605.20514/) (2026)

## Abstract (arXiv)

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.