用拓扑方法统一分析无序材料的局部与全局结构。
Persistent Homology for Structural Characterization in Disordered Systems
- 基于持久同调构建统一算法，同时捕捉局部和全局结构特征。
- 仅用一个变量即可让线性SVM实现近乎完美的三相分类。
- 提出非参数度量分离指数，连接粒子环境与整体相结构。
我们提出一种基于持久同调（Persistent Homology, PH）的统一框架，用于表征无序系统中的局部与全局结构。该方法可使用相同算法与数据结构同时生成局部和全局描述符，在预测粒子重排和分类全局相态方面表现出高度有效性和可解释性。我们还证明，仅用一个变量即可使线性支持向量机（SVM）实现几乎完美的三相分类。受此启发，我们定义了一个非参数度量——分离指数（Separation Index, SI），不仅实现了不损失性能的分类，还建立了粒子环境与全局相结构之间的关联。该方法为理解与分析无序材料的性质提供了有效工具，具有广泛的应用潜力，涵盖材料科学及更广泛的复杂系统研究。
原文摘要 · Abstract (English)
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.
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