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This preprint proposes a graph-recurrent neural network that learns the time evolution of charge-density-wave order in a semiclassical Holstein model directly from simulation trajectories, without explicit equations of motion. It is a proof-of-concept on one model system, so the claims about efficiency and scalability need validation against conventional solvers on larger or more realistic problems. For ML readers, the useful part is the architecture: gated recurrent hidden states combined with graph message passing to capture memory and spatial coupling in learned surrogate dynamics.
Graph-Recurrent Learning of Emergent Collective Dynamics
arXiv:2610.31350v1 Announce Type: cross 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.
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.
Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG)
arXiv:2610.31350 [cond-mat.str-el]
(or arXiv:2610.31350v1 [cond-mat.str-el] for this version)
https://doi.org/10.48550/arXiv.2610.31350 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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