Explainable Machine Learning for Multilayer Planar Winding Inductance Estimation

2026-09-29

AI Summary

This study addresses the complexity of conventional formulas and the poor extrapolation capability of black-box models in estimating the inductance of multi-layer planar windings by proposing the novel SR-KAN framework, which unifies interpretable artificial intelligence with symbolic regression. By integrating SHAP, permutation importance, Kolmogorov–Arnold Networks (KAN), and finite element analysis, this approach automatically derives high-accuracy closed-form analytical equations without requiring predefined structures or prior assumptions. Experimental results demonstrate that the out-of-distribution relative error is reduced to 8.22%, while physical prototype validation yields an average error of only 6.26%, significantly enhancing both generalization performance and physical interpretability. Furthermore, a large-scale dataset comprising simulated and experimentally measured data has been released as open source to facilitate future research.

Abstract

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.

Problem

• Inductance Estimation
• Planar Windings
• Explainable Machine Learning
• Out-of-Distribution Generalization
• High-Frequency Power Converters

Innovation

• Explainable Machine Learning
• Symbolic Regression
• Kolmogorov-Arnold Network
• Out-of-Distribution Generalization
• Planar Winding Inductance