Persistent Homology for Structural Characterization in Disordered Systems

Abstract

We propose a unified framework based on persistent homology (PH) 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 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 SVM to achieve nearly perfect three-phase classification. Inspired by this discovery, we define a non-parametric metric, the Separation Index (SI), 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.

24 pages, 19 figures

References in corpus (17)

• Practical Bayesian Optimization of Machine Learning Algorithms
• On representing chemical environments
• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• A high-bias, low-variance introduction to Machine Learning for physicists
• Identifying structural flow defects in disordered solids using machine learning methods
• Hierarchical structures of amorphous solids characterized by persistent homology
• Approximate analytical description of the nonaffine response of amorphous solids
• Ripser: efficient computation of Vietoris-Rips persistence barcodes
• Avalanches and Dynamical Correlations in supercooled liquids
• Local inversion-symmetry breaking controls the boson peak in glasses and crystals
• Higher-order topological insulators in amorphous solids
• Phase diagram of Kob-Andersen type binary Lennard-Jones mixtures
• Pathways to self-organization: crystallization via nucleation and growth
• Distribution of local relaxation events in an aging 3D glass: spatio-temporal correlation and dynamical heterogeneity
• Persistent homology analysis of osmolyte molecular aggregation and their hydrogen-bonding networks

Cited by in corpus (2)

• Revealing the Void-Size Distribution of Silica Glass using Persistent Homology
• Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics