PINNs for Electromagnetic Wave Propagation
Nilufer K. Bulut
TL;DR
This work demonstrates that Physics-Informed Neural Networks can closely match conventional FDTD results for time-domain electromagnetic wave propagation in a 2D PEC cavity when a hybrid training strategy is employed. By combining time-marching to preserve causality, sequential windowed training with interface continuity constraints, and a local Poynting-based regularizer to enforce energy conservation, the PINN learns accurate field distributions for $E_z$, $H_x$, and $H_y$ without labeled data. The approach achieves sub-percent field errors (average NRMSE around $0.09\%$ and $L_2$ error about $1.01\%$) and energy mismatches on the order of $10^{-2}\%$, with robust performance in a lossy medium as well. These results highlight the importance of embedding physical structure—causality, energy conservation, and interface continuity—directly into the loss function when applying PINNs to electromagnetics, and reveal sensitivity to implementation details such as Poynting formulation (the so-called parenthesis effect). The findings suggest PINNs are a viable mesh-free alternative for canonical EM problems and can extend to inverse or complex geometries with careful loss design.
Abstract
Physics-Informed Neural Networks (PINNs) are a methodology that aims to solve physical systems by directly embedding PDE constraints into the neural network training process. In electromagnetism, where well-established methodologies such as FDTD and FEM already exist, new methodologies are expected to provide clear advantages to be accepted. Despite their mesh-free nature and applicability to inverse problems, PINNs can exhibit deficiencies in terms of accuracy and energy metrics when compared to FDTD solutions. This study demonstrates hybrid training strategies can bring PINNs closer to FDTD-level accuracy and energy consistency. This study presents a hybrid methodology addressing common challenges in wave propagation scenarios. The causality collapse problem in time-dependent PINN training is addressed via time marching and causality-aware weighting. In order to mitigate the discontinuities that are introduced by time marching, a two-stage interface continuity loss is applied. In order to suppress loss accumulation, which is manifested as cumulative energy drift in electromagnetic waves, a local Poynting-based regularizer has been developed. In the developed PINN model, high field accuracy is achieved with an average 0.09\% $NRMSE$ and 1.01\% $L^2$ error over time. Energy conservation is achieved on the PINN side with only a 0.024\% relative energy mismatch in the 2D PEC cavity scenario. Training is performed without labeled field data, using only physics-based residual losses; FDTD is used solely for post-training evaluation. The results demonstrate that PINNs can achieve competitive results with FDTD in canonical electromagnetic examples and are a viable alternative.