Supervised and unsupervised learning of directed percolation

Machine learning (ML) has been well applied to studying equilibrium phase transition models, by accurately predicating critical thresholds and some exponents. Difficulty will be raised, however, for integrating ML into non-equilibrium transitions. The extra dimension in a given system, namely time, can greatly slow down the procedure towards steady state. In this paper we find that using simple techniques of ML, non-steady state configurations directed percolation (DP) suffice capture its essential behaviors both (1+1) (2+1) dimensions. With supervised method, framework our binary classification neural networks identify threshold, as spatial temporal correlation characteristic time $t_{c}$, specifying from active phases absorbing ones, is also major product learning. Moreover, employ convolutional autoencoder, an unsupervised technique, extract dimensionality reduction representations cluster bond DP. It quite appealing such method yield reasonable estimation point.