Machine learning of percolation models using graph convolutional neural networks

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.

Neural network topological snake models for locating general phase diagrams

Machine learning for locating phase diagram has received intensive research interest in recent years. However, its application in automatically locating phase diagram is limited to single closed phase boundary. In this paper, in order to locate phase diagrams with multiple phases and complex boundaries, we introduce (i) a network-shaped snake model and (ii) a topologically transformable snake with discriminative cooperative networks, respectively. The phase diagrams of both quantum and classical spin-1 model are obtained. Our method is flexible to determine the phase diagram with just snapshots of configurations from the cold-atom or other experiments.