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Machine learning for phase transition has received intensive researchinterest in recent years. However, its application in percolation still remainschallenging. We propose an auxiliary Ising mapping method for machine learningstudy of the standard percolation as well as a variety of statisticalmechanical systems in correlated percolation representations. We demonstratethat unsupervised machine learning is able to accurately locate the percolationthreshold, independent of the spatial dimension of system or the type of phasetransition, which can be first order or continuous. Moreover, we show that, byneural network machine learning, auxiliary Ising configurations for differentuniversalities can be classified with high confidence level. Our resultsindicate that the auxiliary Ising mapping method, despite of it simplicity, canadvance the application of machine learning in statistical and condensed-matterphysics.

Machine learning for percolation utilizing auxiliary Ising variables