Supervised and unsupervised learning of directed percolation.

Area of Science:

• Statistical Physics
• Computational Physics
• Machine Learning

Background:

• Machine learning (ML) excels at equilibrium phase transitions but struggles with nonequilibrium systems due to the added time dimension.
• Nonequilibrium systems, such as directed percolation (DP), present challenges for ML due to slow convergence to steady states.

Purpose of the Study:

• To investigate the efficacy of simple machine learning techniques for analyzing nonequilibrium phase transitions.
• To demonstrate that non-steady-state configurations are sufficient for capturing critical behaviors in directed percolation.
• To apply both supervised and unsupervised learning methods for phase transition analysis.

Main Methods:

• Utilized supervised learning with binary classification neural networks to identify phase transition thresholds and critical exponents.
• Employed unsupervised learning via convolutional autoencoders for dimensionality reduction and configuration clustering.
• Applied these ML techniques to directed percolation models in (1+1) and (2+1) dimensions.

Main Results:

• Successfully identified the phase transition threshold and spatial/temporal correlation exponents using supervised learning.
• Determined the characteristic time (t_c) indicating the transition from active to absorbing phases.
• Achieved a reasonable estimation of the critical point using unsupervised learning with convolutional autoencoders.

Conclusions:

• Simple machine learning techniques can effectively analyze critical behaviors in nonequilibrium phase transitions, specifically directed percolation.
• Non-steady-state configurations provide sufficient information for ML models to capture essential critical phenomena.
• Both supervised and unsupervised ML approaches offer valuable tools for understanding complex dynamic systems.