Supervised, semi-supervised, and unsupervised learning of the Domany-Kinzel model

TL;DR

This paper explores various machine learning techniques, including supervised, semi-supervised, and unsupervised methods, to analyze phase transitions and critical behaviors in the (1+1)-dimensional Domany-Kinzel model, a non-equilibrium statistical physics system.

Contribution

It introduces the application of PCA and autoencoders for predicting critical points, alongside traditional supervised and semi-supervised learning, providing new tools for studying phase transitions.

Findings

Supervised learning accurately estimates critical points from labeled data.

Semi-supervised learning effectively uses unlabeled data for critical point estimation.

PCA and autoencoders produce results consistent with particle density simulations.

Abstract

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