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

arXiv: https://arxiv.org/abs/2207.08927 · HTML: https://mlsanity.com/paper/2207.08927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## Builds on (most cited first, 17 of 17)

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- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Dynamic Graph Neural Networks for Sequential Recommendation](https://mlsanity.com/paper/2104.07368/) (2021)
- [Improving Molecular Graph Neural Network Explainability with Orthonormalization and Induced Sparsity](https://mlsanity.com/paper/2105.04854/) (2021)
- [Scalable Graph Networks for Particle Simulations](https://mlsanity.com/paper/2010.06948/) (2020)
- [Competition-induced criticality in a model of meme popularity](https://mlsanity.com/paper/1305.4328/) (2013)
- [Graph network for learning bi-directional physics](https://mlsanity.com/paper/2112.07054/) (2021)

## Abstract (arXiv)

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.