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Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenonbelieved to be responsible for the emergence of universal scale-invariantbehavior in many, seemingly unrelated systems, such as forest fires, virusspreading or atomic excitation dynamics. SOC describes the buildup oflarge-scale and long-range spatio-temporal correlations as a result of onlylocal interactions and dissipation. The simulation of SOC dynamics is typicallybased on Monte-Carlo (MC) methods, which are however numerically expensive anddo not scale beyond certain system sizes. We investigate the use of GraphNeural Networks (GNNs) as an effective surrogate model to learn the dynamicsoperator for a paradigmatic SOC system, inspired by an experimentallyaccessible physics example: driven Rydberg atoms. To this end, we generalizeexisting GNN simulation approaches to predict dynamics for the internal stateof the node. We show that we can accurately reproduce the MC dynamics as wellas generalize along the two important axes of particle number and particledensity. This paves the way to model much larger systems beyond the limits oftraditional MC methods. While the exact system is inspired by the dynamics ofRydberg atoms, the approach is quite general and can readily be applied toother systems.

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