Physics-Informed Neural Networks for 2D Plane Wave Scattering in Arbitrary Dielectric Structures

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.