Scale-Invariant Neural Networks for Percolation

This thesis explores the integration of Renormalization Group theory with Machine Learning to develop a multiscale classifier for predicting square lattice site percolation. The model processes binary lattices of varying sizes, mimicking the iterative RG flow, and demonstrates improved performance when trained on mixed-size data compared to fixed-size training. Key results show that the classifier achieves high accuracy (90–95%) in phase classification, with the arithmetic averaging first coarse-graining (AFC) method proving most effective. The learned coarse-graining rules resemble sigmoidal functions, consistent with theoretical RG expectations, and provide estimates of the percolation threshold (0.569–0.589) close to the known theoretical value. By bridging RG theory with machine learning, this framework offers a physics-informed method for studying critical phenomena.