发表机构
National Technical University of Athens; National and Kapodistrian University of Athens（雅典国立技术大学; 雅典国立卡波季斯特里安大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出结合SHAP、置换重要性与SR-KAN符号回归的可解释ML框架，用于多层平面绕组电感估计，在OOD数据上误差8.22%，硬件验证误差6.26%，并开源数据集。
AI 中文摘要
快速准确地估计多层矩形平面绕组的自感对于现代高频功率变换器至关重要，然而传统工作流程依赖于复杂的数学方程、刚性的单项式公式或不可解释的黑盒机器学习（ML）模型，这些模型在其训练域之外性能严重下降。本文介绍了一个可解释的机器学习框架，该框架通过SR-KAN框架将事后特征归因（SHAP和置换重要性）与Kolmogorov-Arnold网络引导的符号回归相结合，以在无需先验结构假设的情况下发现闭式解析方程。在一个包含超过10,000个有限元分析（FEA）模拟、涵盖七个分布外（OOD）类别的新开源数据集上评估时，标准基于树的集成模型表现出严重的外推误差（>36%），而无约束的SR-KAN表达式实现了稳健的OOD相对误差8.22%。对55个物理印刷电路板原型（最多8层，电感范围从4.11 μH到559.27 μH）的实验验证证实，KAN发现的表达式能有效迁移到真实硬件，预测电感的平均绝对相对误差为6.26%。为支持可复现研究，完整的FEA模拟数据集和原型测量结果已开源发布。
英文摘要
Rapid and accurate self-inductance estimation for multilayer rectangle-shaped planar windings is essential for modern high-frequency power converters, yet traditional workflows rely on complex mathematical equations, rigid monomial formulas or unexplainable black-box machine learning (ML) models that degrade severely outside their training domain. This paper introduces an explainable ML framework unifying post-hoc feature attribution (SHAP and permutation importance) with Kolmogorov-Arnold Network-guided symbolic regression via the SR-KAN framework to discover closed-form analytical equations without prior structural assumptions. Evaluated on a new open-source dataset of over 10,000 Finite Element Analysis (FEA) simulations across seven out-of-distribution (OOD) classes, standard tree-based ensembles exhibit severe extrapolation errors (> 36%), whereas the unconstrained SR-KAN expression achieves a robust OOD relative error of 8.22%. Experimental verification across 55 physical printed circuit board prototypes (up to 8 layers, with inductances from 4.11 μH to 559.27 μH) confirms that the KAN-discovered expression translates effectively to real-world hardware, predicting inductance with a mean absolute relative error of 6.26%. To support reproducible research, the complete FEA simulation dataset and prototype measurements are released open-source.
Comments10 pages
