arXiv 2511.086552026-01-06cs.LGcs.AI

学习基础：一种基于Kolmogorov-Arnold网络的方法，嵌入Green函数先验

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

Key Laboratory of Universal Wireless Communication, Ministry of Education, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications（信息与通信工程学院，北京邮电大学，教育部无线通信重点实验室）；Department of Informatics and Telecommunications, National and Kapodistrian University of Athens（信息与电信学院，希腊国家与卡波迪斯蒂亚纳大学）；telecommunication company in Stockholm, Sweden（瑞典斯德哥尔摩的一家电信公司）；School of Computing, Engineering and Mathematical Sciences, La Trobe University（计算、工程与数学科学学院，拉特罗布大学）

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

备注：: 4 pages, 3 figures. Submitted to IEEE Antennas and Wireless Propagation Letters

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AI总结：

本文提出PhyKAN，一种基于Kolmogorov-Arnold网络的可学习基础方法，通过嵌入Green函数先验，实现高精度电磁建模。

摘要：

方法中的时刻（MoM）受到使用静态、几何定义的基础函数的限制，例如Rao-Wilton-Glisson（RWG）基础。本文信件将电磁建模重新围绕可学习的基础表示而不是在固定基础上求解系数。我们首先表明，RWG基础本质上是Kolmogorov-Arnold表示定理的静态和分段线性实现。受这一见解的启发，我们提出了PhyKAN，一种融合物理的Kolmogorov-Arnold网络（KAN），将RWG推广为可学习和适应性的基础家族。从EFIE导出，PhyKAN整合了一个局部KAN分支和一个嵌入Green函数先验的全局分支，以保持物理一致性。证明了在经典几何中，PhyKAN实现子0.01的重建误差，以及准确的、无监督的雷达截面预测，为经典求解器和现代神经网络模型之间的电磁建模提供了可解释、物理一致的桥梁。

英文摘要：

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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