Neural Renormalization Group Flow for Percolation

Abstract:Machine learning offers a possible route to data-driven real-space renormalization when the relevant observables are nonlocal and difficult to prescribe explicitly. We explore this idea for two-dimensional site percolation developping a supervised, scale-shared neural architecture. The model recursively applies the same learned coarse-graining rule across scales, producing a latent field from which the crossing probability is predicted, while a corresponding fine-graining decoder reconstructs the largest-cluster mask. Trained only on small lattices, the model extrapolates to substantially larger systems, recovers the spanning cluster with high fidelity, and produces observables obeying the expected finite-size scaling near the critical point. We observe that to get such performance it is key that the learned latent representation exhibits critical fluctuations and scale-dependent flows consistent with the renormalization-group structure of percolation.

Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)

arXiv:2608.26764 [cond-mat.dis-nn]

(or arXiv:2608.26764v1 [cond-mat.dis-nn] for this version)

https://doi.org/10.48550/arXiv.2608.26764 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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