The Method of Moments (MoM) is constrained by the usage of static, geometry-defined basis functions, such as the Rao-Wilton-Glisson (RWG) basis. This letter reframes electromagnetic modeling around a learnable basis representation rather than solving for the coefficients over a fixed basis. We first show that the RWG basis is essentially a static and piecewise-linear realization of the Kolmogorov-Arnold representation theorem. Inspired by this insight, we propose PhyKAN, a physics-informed Kolmogorov-Arnold Network (KAN) that generalizes RWG into a learnable and adaptive basis family. Derived from the EFIE, PhyKAN integrates a local KAN branch with a global branch embedded with Green's function priors to preserve physical consistency. It is demonstrated that, across canonical geometries, PhyKAN achieves sub-0.01 reconstruction errors as well as accurate, unsupervised radar cross section predictions, offering an interpretable, physics-consistent bridge between classical solvers and modern neural network models for electromagnetic modeling.

翻译：矩量法（MoM）受限于使用静态的、由几何定义的基函数，例如Rao-Wilton-Glisson（RWG）基函数。本文提出将电磁建模重构为围绕可学习基函数表示的方法，而非在固定基函数上求解系数。我们首先证明RWG基函数本质上是Kolmogorov-Arnold表示定理的一种静态、分段线性实现。受此启发，我们提出PhyKAN——一种物理信息驱动的Kolmogorov-Arnold网络（KAN），它将RWG基函数推广为可学习且自适应的基函数族。基于电场积分方程（EFIE）推导，PhyKAN将局部KAN分支与嵌入格林函数先验的全局分支相结合，以保持物理一致性。实验表明，在典型几何结构上，PhyKAN实现了低于0.01的重构误差以及准确的无监督雷达截面预测，为经典求解器与现代神经网络模型在电磁建模领域搭建了可解释且物理一致的桥梁。