Siamese Neural Network for Label-Efficient Critical Phenomena Prediction in 3D Percolation Models

TL;DR

This paper introduces a Siamese Neural Network that accurately predicts critical phenomena in 3D percolation models with high label efficiency, addressing limitations of previous 2D-focused machine learning methods.

Contribution

The study presents a novel SNN approach that leverages the largest cluster features to improve prediction accuracy and label efficiency in 3D percolation systems.

Findings

Achieves sub-1% error in predicting percolation thresholds and exponents.

Requires significantly fewer labeled samples than traditional methods.

Effective for both site and bond percolation in three dimensions.

Abstract

Percolation theory serves as a cornerstone for studying phase transitions and critical phenomena, with broad implications in statistical physics, materials science, and complex networks. However, most machine learning frameworks for percolation analysis have focused on two-dimensional systems, oversimplifying the spatial correlations and morphological complexity of real-world three-dimensional materials. To bridge this gap and improve label efficiency and scalability in 3D systems, we propose a Siamese Neural Network (SNN) that leverages features of the largest cluster as discriminative input. Our method achieves high predictive accuracy for both site and bond percolation thresholds and critical exponents in three dimensions, with sub-1% error margins using significantly fewer labeled samples than traditional approaches. This work establishes a robust and data-efficient framework for modeling high-dimensional critical phenomena, with potential applications in materials discovery and complex network analysis.