Mapping Hierarchical Motifs in disorder-order transitions: learning structural motifs in supercooled liquids and crystals
5 affiliations
- 1Department of Physics
- 2National University of Singapore
- 3Graduate School for Integrative Sciences and Engineering Programme
- 4Department of Chemical and Biomolecular Engineering
- 5Center for Bio-Imaging Sciences
Abstract
Disorder-order transitions pass through structurally rich intermediates that conventional order parameters cannot fully resolve. Here, we introduce a hierarchical motif framework to characterize structural motifs from nucleation of supercooled water. Inspired by language modeling, our framework learns a discrete vocabulary and a grammar of how motifs interact in space and time. By applying vector quantization (VQ) to the learned embeddings of a variational autoencoder (VAE) trained on the structural descriptors, we establish a vocabulary of motifs comprising discrete labels of liquid, transient, and ice motifs. Moreover, the VAE quantifies local disorder that decreases from liquid to ice motifs. Analysis of the motif grammar, including motif-motif transitions, spatial co-occurrences, and ring occupancies, unifies mechanistic descriptions of the spatiotemporal dynamics of ice nucleation. The transient motifs resolve two structural roles: locally-ordered low-density (LD) environments that constitute precursors during supercooling, and non-consolidating interfacial regions. These LD precursors organize into a continuum of ring networks, revealing two processes during nucleation: trimers/tetramers continuously re-organize into closed pentamers/hexamers in ring scaffolds, while atomwise motifs relabel in bursts along an energy ladder. Next, we extend the motif framework to characterize metastable motifs formed by hypothetical polymorphs in heterogeneous nucleation simulations, which elucidates how structural motifs at the ice/liquid interface control ice nucleation. Beyond disorder-order transitions in supercooled water, we further demonstrate the generality of our framework in characterizing transitions in the nucleation of silicon and liquid-liquid transition of water.
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BibTeX
@misc{yue2026mapping,
title = {{Mapping Hierarchical Motifs in disorder-order transitions: learning structural motifs in supercooled liquids and crystals}},
author = {Yifei Yue and Lechun Xing and Saad Aldin Mohammed and Jianwen Jiang and N. Duane Loh},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15004179/v3},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15004179/v3},
note = {CC BY},
}
RIS
TY - UNPB
TI - Mapping Hierarchical Motifs in disorder-order transitions: learning structural motifs in supercooled liquids and crystals
AU - Yifei Yue
AU - Lechun Xing
AU - Saad Aldin Mohammed
AU - Jianwen Jiang
AU - N. Duane Loh
PY - 2026
DA - 2026/10/22
PB - ChemRxiv
DO - 10.26434/chemrxiv.15004179/v3
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15004179/v3
AB - Disorder-order transitions pass through structurally rich intermediates that conventional order parameters cannot fully resolve. Here, we introduce a hierarchical motif framework to characterize structural motifs from nucleation of supercooled water. Inspired by language modeling, our framework learns a discrete vocabulary and a grammar of how motifs interact in space and time. By applying vector quantization (VQ) to the learned embeddings of a variational autoencoder (VAE) trained on the structural descriptors, we establish a vocabulary of motifs comprising discrete labels of liquid, transient, and ice motifs. Moreover, the VAE quantifies local disorder that decreases from liquid to ice motifs. Analysis of the motif grammar, including motif-motif transitions, spatial co-occurrences, and ring occupancies, unifies mechanistic descriptions of the spatiotemporal dynamics of ice nucleation. The transient motifs resolve two structural roles: locally-ordered low-density (LD) environments that constitute precursors during supercooling, and non-consolidating interfacial regions. These LD precursors organize into a continuum of ring networks, revealing two processes during nucleation: trimers/tetramers continuously re-organize into closed pentamers/hexamers in ring scaffolds, while atomwise motifs relabel in bursts along an energy ladder. Next, we extend the motif framework to characterize metastable motifs formed by hypothetical polymorphs in heterogeneous nucleation simulations, which elucidates how structural motifs at the ice/liquid interface control ice nucleation. Beyond disorder-order transitions in supercooled water, we further demonstrate the generality of our framework in characterizing transitions in the nucleation of silicon and liquid-liquid transition of water.
ER -