Physics-Informed Neural Networks for Solving Maxwell’s Equations in Electromagnetic Wave Propagation

Maryam Nihad Salem (Diyala University, Postgraduate studies, Diyala)
Nebras Jalel Ibrahim (Diyala University, Computer Center, Diyala)
Walaa Badr Khudhair (Diyala University, Computer Center, Diyala)
Hassan Al-Mahdawi (Diyala University, Computer Center, Diyala)
Zainab Hassan Mohammed (Diyala University, Computer Center, Diyala)
Zainab khazal Shamel (Diyala University, Al-Miqdad College of Education, Diyala)
Alaulddin Mueen Latfa (Baghdad)

Academia Open
Vol. 10 No. 2 (2025): December

General background: Electromagnetic wave modeling is essential for modern communication systems, yet classical numerical solvers such as FDTD, FEM, and MoM often face high computational cost and meshing limitations. Specific background: Recent advances in physics-informed machine learning offer new approaches to solving Maxwell’s equations through continuous, mesh-free models. Knowledge gap: Despite growing interest, the performance, accuracy, and scalability of Physics-Informed Neural Networks (PINNs) for full-wave electromagnetic propagation remain insufficiently validated against established numerical solvers. Aims: This study develops a PINN framework that embeds Maxwell’s PDEs, initial conditions, and boundary constraints directly into a unified loss function to model one-dimensional wave propagation. Results: The proposed PINN achieves <1% relative error compared with an FDTD reference, demonstrates stable convergence, accurately reproduces wave propagation and reflections, and performs 100× faster during inference while using 40% less memory. Novelty: The model provides a continuous, differentiable electromagnetic field representation without discretization, enabling physically consistent predictions and fast generalization to different boundaries or materials. Implications: These results highlight PINNs as a promising mesh-free alternative for real-time electromagnetic analysis, with scalability toward higher-dimensional waveguides, antennas, and inverse design applications.Highlight : PINNs incorporate Maxwell’s PDE residuals directly into training to ensure physically consistent electromagnetic field predictions. The model achieves accuracy comparable to classical solvers while reducing computational load and avoiding mesh constraints. Results demonstrate reliable wave propagation, reflection behavior, and high numerical stability within the simulated domain. Keywords : Physics-informed neural networks, Maxwell’s equations, electromagnetic propagation, wave modeling, mesh-free computation