Persistent Homology for Structural Characterization in Disordered Systems

2024-11-21

arXiv.org

AI Summary

Addressing the challenges of characterizing structural disorder and predicting dynamics in amorphous systems, this work proposes a unified topological analysis framework based on persistent homology (PH). Methodologically, it simultaneously extracts both local and global topological features; introduces a non-parametric Separation Index (SI) that directly links particle-level local environments to macroscopic phase structures; and employs univariate PH descriptors to drive linear support vector machine (SVM) classification. Key contributions include: (i) the first demonstration of near-perfect (≈100%) three-phase linear classification using a single topological metric; and (ii) substantially improved interpretability and cross-system generalizability in predicting particle rearrangement events. This study establishes a general, parsimonious, and interpretable topological analysis paradigm specifically tailored for disordered materials.

Technology Category

• Machine Learning: Learning with Manifolds
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Interdisciplinary science discovery with web data mining
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

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.

Problem

• Persistent Homology
• Complex Systems
• Particle Motion Prediction

Innovation

• Persistent Homology
• Separation Index (SI)
• Complex Disordered Systems