Machine learning of pair-contact process with diffusion.

Area of Science:

• Statistical Physics
• Non-equilibrium Phase Transitions
• Computational Physics

Background:

• The pair-contact process with diffusion (PCPD) is a generalized model of the pair-contact process (PCP).
• The phase transition of PCPD is controversial, with no consensus on its universality class.
• Existing research lacks a definitive classification for PCPD's non-equilibrium phase transition.

Purpose of the Study:

• To investigate the phase transition of the pair-contact process with diffusion (PCPD) using machine learning.
• To determine if PCPD belongs to known universality classes or represents a new type of phase transition.
• To apply both unsupervised and supervised learning for a comprehensive analysis.

Main Methods:

• Employed unsupervised learning techniques: Principal Component Analysis (PCA) and autoencoders.
• Utilized supervised learning to analyze PCPD at varying diffusion rates.
• Developed an improved numerical method for determining the spatial correlation exponent.

Main Results:

• Unsupervised learning methods successfully clustered model configurations and estimated critical thresholds.
• Both PCA and autoencoders demonstrated the ability to extract essential hidden information from non-equilibrium lattice models.
• The proposed numerical method provided more accurate estimates of the spatial correlation exponent, reducing data collapse uncertainties.

Conclusions:

• Machine learning, particularly unsupervised learning, offers a robust approach to studying complex non-equilibrium systems like PCPD.
• These methods can effectively identify critical phenomena and extract underlying patterns in models with or without diffusion.
• The findings contribute to a better understanding of non-equilibrium phase transitions and provide tools for future research in statistical physics.