Unsupervised learning of site percolation based on shuffled configurations

In the field of statistical physics, machine learning has gained significant popularity and has achieved remarkable results in recent studies on phase transitions.In this paper, we apply Principal Component Analysis (PCA) and Autoencoder(AE) based on Unsupervised learning to study the various configurations of the percolation model in equilibrium phase transition. In certain phase transition models, such as the DP model in non-equilibrium phase transitions, the order parameter is particle density. However, in some other phase transition models, such as the percolation model, it is not. This study involved randomizing and selecting percolation graphs to be used as input for a neural network, and analyzed the obtained results, indicating that the outputs of the single latent variable of AE and the first principal component of PCA are signals related to particle density.