Machine learning of percolation models using graph convolutional neural networks

TL;DR

This paper develops a graph convolutional neural network framework to predict and analyze percolation thresholds across different lattice types, advancing machine learning applications in complex systems modeling.

Contribution

It introduces a novel GCN-based approach for both supervised and unsupervised percolation analysis, capable of handling multiple lattice types and accurately estimating thresholds.

Findings

GCN effectively trains on various lattice data

Unsupervised method identifies percolation thresholds via 'W' performance shape

Framework enables general analysis of percolation phenomena

Abstract

Percolation is an important topic in climate, physics, materials science, epidemiology, finance, and so on. Prediction of percolation thresholds with machine learning methods remains challenging. In this paper, we build a powerful graph convolutional neural network to study the percolation in both supervised and unsupervised ways. From a supervised learning perspective, the graph convolutional neural network simultaneously and correctly trains data of different lattice types, such as the square and triangular lattices. For the unsupervised perspective, combining the graph convolutional neural network and the confusion method, the percolation threshold can be obtained by the "W" shaped performance. The finding of this work opens up the possibility of building a more general framework that can probe the percolation-related phenomenon.