Explainable machine learning improves multilayer planar winding inductance estimation
Explainable Machine Learning for Multilayer Planar Winding Inductance Estimation
Machine Learning
Summary
Estimating the inductance of multilayer planar windings quickly and accurately is important for modern electronics but is usually done with complex math or black-box models that can be unreliable. The authors combine explainable machine learning techniques with symbolic regression to discover simple, interpretable formulas that predict inductance well. Tested on a large simulated dataset and real hardware prototypes, their method greatly reduces error compared to traditional approaches. They also provide their simulation data and measurements openly for others to use.
What this means in practice
- •For power electronics engineers: Use interpretable formulas to quickly and accurately estimate inductance of multilayer planar windings during power converter design.
- •For pcb designers: Predict inductance values of planar windings on printed circuit boards with improved accuracy to optimize hardware performance.
Authors
Spyros Rigas, Theofilos Papadopoulos, Georgios Alexandridis, Antonios Antonopoulos
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.