Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks

TL;DR

This paper demonstrates that Graph Neural Networks can effectively learn and simulate the dynamics of self-organized criticality in Rydberg atoms, enabling scalable modeling of large systems beyond traditional Monte-Carlo methods.

Contribution

The authors develop a GNN-based surrogate model that accurately predicts SOC dynamics in Rydberg atoms and generalizes across system sizes and densities.

Findings

GNNs accurately reproduce Monte-Carlo dynamics

Model generalizes to larger particle numbers and densities

Enables scalable simulation of SOC systems

Abstract

Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenon believed to be responsible for the emergence of universal scale-invariant behavior in many, seemingly unrelated systems, such as forest fires, virus spreading or atomic excitation dynamics. SOC describes the buildup of large-scale and long-range spatio-temporal correlations as a result of only local interactions and dissipation. The simulation of SOC dynamics is typically based on Monte-Carlo (MC) methods, which are however numerically expensive and do not scale beyond certain system sizes. We investigate the use of Graph Neural Networks (GNNs) as an effective surrogate model to learn the dynamics operator for a paradigmatic SOC system, inspired by an experimentally accessible physics example: driven Rydberg atoms. To this end, we generalize existing GNN simulation approaches to predict dynamics for the internal state of the node. We show that we can accurately reproduce the MC dynamics as well as generalize along the two important axes of particle number and particle density. This paves the way to model much larger systems beyond the limits of traditional MC methods. While the exact system is inspired by the dynamics of Rydberg atoms, the approach is quite general and can readily be applied to other systems.