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Persistent homology for structural characterization in disordered systems

An Wang1,* and Li Zou2

  • *Contact author: amturing@outlook.com
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Phys. Rev. E 111, 045306 – Published 17 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.045306

Abstract

We propose a unified framework based on persistent homology to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data structure, and has been shown to be highly effective and interpretable in predicting particle rearrangements and classifying global phases. We also demonstrated that using a single variable enables a linear support vector machine to achieve nearly perfect three-phase classification. Inspired by this discovery, we define a nonparametric metric, the separation index, which not only achieves this classification without sacrificing significant performance but also establishes a connection between particle environments and the global phase structure. Our methods provide an effective framework for understanding and analyzing the properties of disordered materials, with broad potential applications in materials science and even wider studies of complex systems.

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Corrections

17 July, 2025

Correction: The second sentence in the third paragraph of Sec. II A 3 contained an error in wording and has been fixed.

Article Text

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Phys. Rev. E 111, 045306– Published 17 April, 2025
  • Received 22 November 2024
  • Accepted 21 March 2025
  • Corrected 17 July 2025
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