Supervised and unsupervised learning of directed percolation

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.

arXiv comment14 pages, 12 figures

References in corpus (18)

• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Machine learning phases of matter
• A high-bias, low-variance introduction to Machine Learning for physicists
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Machine learning quantum phases of matter beyond the fermion sign problem
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Universal scaling behavior of non-equilibrium phase transitions
• The Field Theory Approach to Percolation Processes
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Machine learning of phase transitions in the percolation and XY models
• Forest fires and other examples of self-organized criticality
• Numerical Study of Local and Global Persistence in Directed Percolation
• High-precision Monte Carlo study of directed percolation in (d+1) dimensions
• Self-Organized Critical Directed Percolation

Cited by in corpus (14)

• Transfer learning of phase transitions in percolation and directed percolation
• The percolating cluster is invisible to image recognition with deep learning
• Study of phase transition of Potts model with Domain Adversarial Neural Network
• Phase determination with and without deep learning
• Machine learning of phases and structures for model systems in physics
• Principal component analysis of absorbing state phase transitions
• Run-and-tumble chemotaxis using reinforcement learning
• A simple framework for contrastive learning phases of matter
• Minimalist Neural Networks training for phase classification in diluted-Ising models
• Learning phase transitions by siamese neural network
• Exploring percolation phase transition in the three-dimensional Ising model with machine learning
• Diagnosing quantum transport from wave function snapshots
• Physical meaning of principal component analysis for classical lattice systems with translational invariance
• Hierarchy of percolation patterns in a kinetic replication model