Explainable Machine Learning for Multilayer Planar Winding Inductance Estimation

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 {\mu}H to 559.27 {\mu}H) 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.

Machine Learning (cs.LG)

arXiv:2609.37211 [cs.LG]

(or arXiv:2609.37211v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.37211 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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