arXiv:2512.23396physics.comp-phcs.AI2025-12

PINN通过混合训练策略实现电磁波传播的高精度模拟,媲美传统方法。

PINNs for Electromagnetic Wave Propagation

  • 结合时间推进与因果感知加权,解决时序训练中的因果崩溃问题。
  • 平均0.09% NRMSE和1.01% L²误差,能量匹配仅0.02%偏差。
  • 无需标注数据,纯物理损失训练,适合电磁逆问题与无网格场景。

物理信息神经网络(PINNs)通过将控制偏微分方程直接嵌入神经网络训练来求解物理系统。在电磁学领域,尽管已有如时域有限差分法(FDTD)和有限元法(FEM)等成熟方法,新方法需具备明确优势才能被采纳。尽管PINNs具有无网格特性且适用于反问题,但在精度和能量守恒方面仍常逊于FDTD。本研究展示,混合训练策略可使PINNs逼近FDTD的精度与能量一致性。提出一种针对电磁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缓解时序训练中的因果崩溃;为消除时间推进引入的不连续性,采用两阶段界面连续性损失;为抑制电磁波累积能量漂移,设计基于局部坡印廷矢量的正则化项。所提出的PINN模型在2D PEC腔体场景中实现平均0.09% NRMSE和1.01% $L^2$误差,能量守恒相对偏差仅为0.02%。训练仅依赖物理残差损失,无需标注场数据,FDTD仅用于后处理评估。结果表明,PINNs在典型电磁场景下可达到与FDTD相当的性能,是一种可行的替代方案。

原文摘要 · Abstract (English)

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.

PINN电磁波物理信息无网格

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