# Machine learning of percolation models using graph convolutional neural networks

arXiv: https://arxiv.org/abs/2207.03368 · HTML: https://mlsanity.com/paper/2207.03368/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 37 references that are in the map.
- First posted on arXiv 7 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)

## Abstract (arXiv)

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.