Neural Renormalization Group Flow for Percolation

2026-08-27

AI Summary

本文通过开发一种监督式的、尺度共享的神经架构，解决了二维点渗流中难以显式描述的相关观测问题，并能够预测跨越概率和重构最大簇。

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.

Problem

• Neural Renormalization
• Percolation
• Machine Learning
• Real-space Renormalization
• Nonlocal Observables

Innovation

• Neural Renormalization Group
• Percolation
• Latent Representation
• Scale-dependent Flows
• Supervised Learning