Supervised and unsupervised learning of directed percolation

TL;DR

This paper demonstrates that simple machine learning techniques can effectively identify critical behaviors and thresholds in directed percolation models, even from non-steady state configurations, in both (1+1) and (2+1) dimensions.

Contribution

It introduces supervised and unsupervised ML methods to analyze non-equilibrium phase transitions, capturing critical thresholds and exponents from early configurations.

Findings

Supervised learning accurately identifies phase transition thresholds.

ML captures spatial and temporal correlation exponents.

Unsupervised autoencoders estimate critical points from early configurations.

Abstract

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