发表机构
LISN; Université Paris-Saclay; Inria Saclay（巴黎南部高等师范学院实验室; 巴黎萨克雷大学; 法国国家信息与自动化研究所萨克雷分所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究开发了一种监督式尺度共享神经架构，用于二维位点渗流，可从小晶格外推至大系统，高保真恢复跨越团簇，其潜在表示的临界涨落与渗流重整化群结构一致。
AI 中文摘要
当相关可观测量是非局域的且难以明确规定时，机器学习为数据驱动的实空间重整化提供了可行途径。针对二维位点渗流，我们开发了一种监督式、尺度共享的神经架构。该模型跨尺度递归应用相同的学习粗粒化规则，生成潜在场以预测穿越概率，同时对应的细粒化解码器重构最大团簇掩码。仅在小晶格上训练的模型可外推至大得多的系统，高保真度地恢复跨越团簇，且在临界点附近产生满足预期有限尺寸标度的可观测量。我们发现，要获得此类性能，关键在于学习到的潜在表示展现出与渗流重整化群结构一致的临界涨落和尺度依赖流。
英文摘要
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.
Comments7 pages, 5 figures
