# Explainable Machine Learning for Multilayer Planar Winding Inductance Estimation

arXiv: https://arxiv.org/abs/2609.37211 · HTML: https://mlsanity.com/paper/2609.37211/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [A Data-Centric Perspective on Evaluating Machine Learning Models for Tabular Data](https://mlsanity.com/paper/2407.02112/) (2024)
- [Inductance Estimation for High-Power Multilayer Rectangle Planar Windings](https://mlsanity.com/paper/2507.12082/) (2025)

## Abstract (arXiv)

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.