Graph-Recurrent Learning of Emergent Collective Dynamics
Abstract
Collective ordering in correlated electron systems emerges from microscopic dynamics, yet the evolution of observable textures need not admit a closed, memoryless description. We introduce a graph-recurrent neural network (GRNN) framework that learns such emergent dynamics directly from trajectories without specifying microscopic equations of motion. The framework integrates gated recurrent memory with graph message passing: local hidden states encode information beyond the instantaneous observables, while spatial coupling allows this information to propagate between sites. The observable and hidden fields evolve jointly through a shared local rule, providing a scalable representation of dynamics with spatial interactions and temporal memory. We demonstrate this framework on the emergent dynamics of charge-density-wave order in the semiclassical Holstein model, successfully reproducing temporal and spatial correlations and dynamical scaling during domain coarsening. By learning finite-time evolution directly, the GRNN offers a route to efficient, data-driven descriptions of collective dynamics with unresolved microscopic degrees of freedom.
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BibTeX
@misc{rayat2026graphrecurrent,
title = {{Graph-Recurrent Learning of Emergent Collective Dynamics}},
author = {Ali Rayat and Acacia Lee and Gia-Wei Chern},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31350},
eprint = {2610.31350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31350},
}
RIS
TY - UNPB
TI - Graph-Recurrent Learning of Emergent Collective Dynamics
AU - Ali Rayat
AU - Acacia Lee
AU - Gia-Wei Chern
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31350
UR - https://arxiv.org/abs/2610.31350
AB - Collective ordering in correlated electron systems emerges from microscopic dynamics, yet the evolution of observable textures need not admit a closed, memoryless description. We introduce a graph-recurrent neural network (GRNN) framework that learns such emergent dynamics directly from trajectories without specifying microscopic equations of motion. The framework integrates gated recurrent memory with graph message passing: local hidden states encode information beyond the instantaneous observables, while spatial coupling allows this information to propagate between sites. The observable and hidden fields evolve jointly through a shared local rule, providing a scalable representation of dynamics with spatial interactions and temporal memory. We demonstrate this framework on the emergent dynamics of charge-density-wave order in the semiclassical Holstein model, successfully reproducing temporal and spatial correlations and dynamical scaling during domain coarsening. By learning finite-time evolution directly, the GRNN offers a route to efficient, data-driven descriptions of collective dynamics with unresolved microscopic degrees of freedom.
ER -