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

TL;DR

This paper introduces PhyKAN, a learnable basis network inspired by the Kolmogorov-Arnold theorem, which improves electromagnetic modeling by integrating physics-informed priors and achieving high accuracy in geometry reconstruction and radar cross section prediction.

Contribution

It reinterprets the classical basis functions as a learnable, adaptive network, bridging traditional electromagnetic solvers with neural network approaches.

Findings

Achieves sub-0.01 reconstruction errors across geometries.

Provides accurate, unsupervised radar cross section predictions.

Offers an interpretable, physics-consistent modeling framework.

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.