Characterizing Atomistic Transitions Using Cross-scale Graph-pooled Chebyshev Signatures

Abstract

Large-scale atomistic simulations can produce extreme volumes of information in the form of long trajectories. Reliably and automatically extracting key information from such datasets remains a formidable challenge, especially as it pertains to the analysis of the structural transitions affecting the system. We present a novel approach to characterize and compare atomistic transitions using cross-scale graph-pooled Chebyshev signatures. These signatures are permutation invariants of an operator that transform a Coulomb matrix representation of the initial state of the system into that corresponding to the final state. Using a long-time trajectory of a small metallic nanoparticle, we show that these signatures can be used to define a natural distance metric between transitions that allows for classification and clustering into physically meaningful families. This approach is shown to capture complex patterns and hierarchies of transition types that are inaccessible to traditional techniques, dramatically facilitating the analysis of large-scale simulations.

Figures (13)

• Figure 1: A visualization of the graph smoothing operator $\mathbf{G}$ operating on a single atom within a configuration at different values of $\tau =0,1,5,10$. Darker colors indicate low values, while brighter colors indicate high values; this convention is followed throughout the manuscript. Short time operators are very local probes of spatial correlations, while longer times capture larger structures.
• Figure 2: Absolute values of $\mathbf{A}_1$ for an arbitrary transition. Atoms are colored by diagonal entries and bonds by the off-diagonal entries.
• Figure 3: Illustration of the target trajectory. Top: Transition IDs are plotted as a function of the transition number; the transition IDs were reordered based on the leaf ordering of the dendrogram obtained from average linkage hierarchical clustering. Bottom: State ID vs transition number. States and transitions are colored according to their primary PCCA cluster, as identified by the GPCCA algorithm with $K_\mathrm{PCCA}=19$ super-states.
• Figure 4: Top: A t-SNE maaten2008visualizing projection of the transition subset colored by the clusters formed by each linkage at $k=12$. While complete linkage seems to visually cluster better, it is important to note that t-SNE plots follow from complex non-linear mappings of the distance matrices that do not necessarily provide a complete and unbiased picture of the data. Bottom: Corresponding distance matrices sorted by dendrogram leaf order. Cophenetic correlation coefficients for each clustering is reported in the title of each column.
• Figure 5: The unsorted distance matrix generated from taking the Wasserstein distance between the cross-scale energy signatures.