Graph coloring with physics-inspired graph neural networks

We show how graph neural networks can be used to solve the canonical coloring problem. frame as a multiclass node classification problem and utilize an unsupervised training strategy based on statistical physics Potts model. Generalizations other problems such community detection, data clustering, minimum clique cover are straightforward. provide numerical benchmark results illustrate our approach with end-to-end application for real-world scheduling use case within comprehensive encode-process-decode framework. Our optimization performs par or outperforms existing solvers, ability scale millions of variables.