AI 中文总结
本文提出无网格物理信息神经网络框架求解二维非均匀介质电磁波散射，将麦克斯韦方程与辐射边界条件嵌入损失函数，经双曲正切平滑函数优化TE偏振精度，对多种结构表现稳定，可高效解决复杂电磁散射问题。
AI 中文摘要
本文提出一种无网格的物理信息神经网络计算框架，用于求解非均匀介质中的二维电磁波散射问题。该框架将频域麦克斯韦方程和辐射边界条件直接嵌入神经网络的损失函数，可针对多种介质构型，准确预测横磁（TM）和横电（TE）偏振的散射场。将该方法应用于单圆柱、同心多层圆柱壳、三个任意排列圆柱及复合不规则结构，结果显示，对于TM偏振，所有相对L²误差大多保持在极低水平，不超过0.1；对于TE偏振，散射体介电特性的急剧变化会导致控制方程出现奇点，使方法精度下降，通过在介质边界引入双曲正切平滑函数可克服这一挑战，该步骤显著提升了方法精度，对应结果与时域有限差分法的预测高度吻合。该框架在所有研究构型中均表现出稳定的收敛行为，证实了其对复杂电磁散射问题的鲁棒性和可扩展性。
英文摘要
In this paper, we introduce a meshless physics-informed neural network based computational framework for solving two-dimensional electromagnetic wave scattering in inhomogeneous media. The framework embeds frequency-domain Maxwell equations and radiation boundary conditions directly into the neural network loss function, enabling accurate prediction of scattered fields for both transverse magnetic (TM) and transverse electric (TE) polarizations across various dielectric configurations. Application of the method to single-cylinder, concentric multilayer cylindrical shells, three arbitrarily arranged cylinders, and composite irregular structures demonstrates that for the TM polarization, all relative $L^{2}$ errors mostly remain at particularly low levels of $\le0.1$. For the TE polarization, sharp variations of the dielectric properties of scatterers lead to singularities in the governing equations, which result in decreased accuracy of the method. This challenge is overcome by introducing at dielectric boundaries a hyperbolic-tangent smoothing function. This procedure significantly improves the accuracy of the method, with the corresponding results closely matching the predictions of the finite-difference time-domain method. This framework exhibits stable convergence behavior across all of the investigated configurations, thus confirming its robustness and scalability to complex electromagnetic scattering problems.
Comments11 pages, 7 figures
