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.

翻译：渗流是气候学、物理学、材料科学、流行病学、金融学等领域的重要课题。利用机器学习方法预测渗流阈值仍具有挑战性。本文构建了一种强大的图卷积神经网络，以监督和无监督两种方式研究渗流现象。从监督学习角度看，该图卷积神经网络能够同时且正确地对不同晶格类型（如方格晶格和三角晶格）的数据进行训练。从无监督角度而言，结合图卷积神经网络与混淆方法，可通过"W"形性能曲线获取渗流阈值。本工作为构建能够探测渗流相关现象的通用框架开辟了可能性。