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arXiv · 2511.08655

Learning the Basis: A Kolmogorov-Arnold Network Approach Embedding Green's Function Priors

Rui Zhu·Yuexing Peng·George C. Alexandropoulos·Wenbo Wang·Wei Xiang
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Abstract

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.

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Rui Zhu, Yuexing Peng, George C. Alexandropoulos, Wenbo Wang, Wei Xiang. 2025-11-11. Learning the Basis: A Kolmogorov-Arnold Network Approach Embedding Green's Function Priors. https://arxiv.org/abs/2511.08655

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