Graph recurrent networks learn complex collective dynamics from data
Graph-Recurrent Learning of Emergent Collective Dynamics
Machine Learning
Summary
Some physical systems show complex patterns that change over time, but it’s hard to describe these changes using simple rules. The authors created a special kind of neural network that looks at both space and time to learn how these patterns evolve, without needing to know the tiny details behind them. They tested their method on a model showing how certain charge patterns form and grow, and their network successfully copied the real behavior. This approach could help understand and predict complex behaviors when the underlying details are unknown or too complicated.
What this means in practice
- •For materials simulation teams: Create efficient data-driven models to predict complex material behaviors without detailed microscopic equations.
- •For complex systems engineers: Model and simulate collective behaviors in spatially distributed systems using learned dynamics from observed data.
Authors
Ali Rayat, Acacia Lee, Gia-Wei Chern
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.