Supervised, semisupervised, and unsupervised learning of the Domany-Kinzel model

The Domany-Kinzel (DK) model encompasses several types of nonequilibrium phase transitions, depending on the selected parameters. We apply supervised, semisupervised, and unsupervised learning methods to studying the phase transitions and critical behaviors of the $(1+1)$-dimensional DK model. The supervised and the semisupervised learning methods permit the estimations of the critical points, the spatial and temporal correlation exponents, concerning labeled and unlabeled DK configurations, respectively. Furthermore, we also predict the critical points by employing principal component analysis and autoencoder. The PCA and autoencoder can produce results in good agreement with simulated stationary particle number density.