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.

翻译：物理信息神经网络通过将控制偏微分方程直接融入神经网络训练来解决物理系统问题。在电磁学领域，尽管已存在如FDTD和FEM等成熟方法，新方法仍需展现明显优势才能被广泛接受。尽管PINNs具有无网格特性且适用于反问题求解，但其在精度和能量指标方面仍可能逊于FDTD。本研究证明，混合训练策略能使PINNs接近FDTD级别的精度与能量一致性。本文提出一种针对波传播常见挑战的混合方法：通过时间推进与因果感知加权解决瞬态PINN训练中的因果性崩溃问题；采用两阶段界面连续性损失缓解时间推进引入的间断性；开发基于局部坡印廷矢量的正则化器以抑制电磁波累积能量漂移。在所开发的PINN模型中，实现了随时间平均0.09% NRMSE与1.01% $L^2$误差的高场精度，在二维PEC腔体场景中仅产生0.02%的相对能量失配。训练过程无需标注场数据，仅使用基于物理的残差损失；FDTD仅用于训练后评估。结果表明，在经典电磁算例中PINNs可获得与FDTD相当的结果，是一种可行的替代方案。