PINNs for Electromagnetic Wave Propagation

TL;DR

This paper enhances Physics-Informed Neural Networks (PINNs) for electromagnetic wave simulation by introducing hybrid training strategies that improve accuracy and energy conservation, making PINNs competitive with traditional methods like FDTD.

Contribution

The study presents a hybrid training methodology for PINNs that addresses accuracy, causality, and energy conservation issues in electromagnetic wave propagation.

Findings

PINNs achieved 0.09% NRMSE in field accuracy.

Energy conservation with 0.02% energy mismatch in 2D PEC cavity.

Hybrid strategies significantly improve PINN performance.

Abstract

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. 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 accuracy and energy metrics compared to FDTD. This study demonstrates that hybrid training strategies can bring PINNs closer to FDTD-level accuracy and energy consistency. A hybrid methodology addressing common challenges in wave propagation is presented. Causality collapse in time-dependent PINN training is addressed via time marching and causality-aware weighting. To mitigate discontinuities introduced by time marching, a two stage interface continuity loss is applied. To suppress cumulative energy drift in electromagnetic waves, a local Poynting-based regularizer is 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 with only a 0.02% 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.