Transfer learning of phase transitions in percolation and directed percolation

Shen, Jianmin; Liu, Feiyi; Chen, Shiyang; Xu, Dian; Chen, Xiangna; Deng, Shaoli; Li, Wei; Papp, Gábor; Yang, C. B.

doi:10.1103/physreve.105.064139

Cited by 5 publications

(3 citation statements)

References 33 publications

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“…Common methods for studying BAW include mean-field [52], master equation [39], and Monte Carlo simulations [53]. For a one-dimensional BAW, we applied the ML approach to study the case of m = 1 in [17,18], termed as (1 + 1)-dimensional DP model. We now shift our focus to the case of even numbers of m, termed as BAW with m-offspring which belongs to the PC universality class.…”

Section: The Model Of Bawmentioning

confidence: 99%

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Supervised and unsupervised learning of (1+1) -dimensional even-offspring branching annihilating random walks

Wang,

Li,

Liu

et al. 2024

Mach. Learn.: Sci. Technol.

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Machine learning (ML) of phase transitions (PTs) has gradually become an effective approach that enables us to explore the nature of various PTs more promptly in equilibrium and nonequilibrium systems. Unlike equilibrium systems, non-equilibrium systems display more complicated and diverse features because of the extra dimension of time, which is not readily tractable, both theoretically and numerically. The combination of ML and most renowned nonequilibrium model, directed percolation (DP), led to some significant findings. In this study, ML is applied to (1+1)-d, even offspring branching annihilating random walks (BAW), whose universality class is not DP-like. The supervised learning of (1+1)-d BAW via convolutional neural networks (CNN) results in a more accurate prediction of the critical point than the Monte Carlo (MC) simulation for the same system sizes. The dynamic exponent \;$z$\; and spatial correlation length correlation exponent \;$\nu_{\perp}$\ were also measured and found to be consistent with their respective theoretical values. Furthermore, the unsupervised learning of (1+1)-d BAW via an autoencoder (AE) gives rise to a transition point, which is the same as the critical point. The latent layer of AE, through a single neuron, can be regarded as the order parameter of the system being properly re-scaled. Therefore, we believe that ML has exciting application prospects in reaction-diffusion systems such as BAW and DP.

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Section: The Model Of Bawmentioning

confidence: 99%

“…As the two main paradigms of ML, supervised and unsupervised learning have shown good performance in the study of equilibrium [14,15] and nonequilibrium [16,17] phase transition models. Supervised learning is mainly used to identify or classify the phases of matter [3,18], where the input data must be labeled.…”

Section: Introductionmentioning

confidence: 99%

Supervised and unsupervised learning of (1+1) -dimensional even-offspring branching annihilating random walks

Wang,

Li,

Liu

et al. 2024

Mach. Learn.: Sci. Technol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…While computational methods, exemplified by Monte Carlo(MC) simulations 9 , have been deployed for studying phase transitions for many years, the application of ML techniques represents a more recent advancement. Initially, in the nascent stages of computationally studying phase transitions, the primary emphasis was placed on the utilization of traditional computational physics techniques such as MC simulations, molecular dynamics [17][18][19] , and density functional theory 20,21 . These methodologies primarily entailed deterministic or statistical approaches.…”

Section: Introductionmentioning

confidence: 99%

Particle density and critical point for studying site percolation by finite size scaling

Xu,

Wang,

Gao

et al. 2024

Preprint

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Machine learning has recently achieved remarkable success in studying phase transitions. It is generally believed that the latent variables of unsupervised learning can capture the information related to phase transitions, which is usually achieved through the so-called order parameter. In most models, for instance the Ising, the order parameters are simply the particle number densities. The percolation, the simplest model which can generate a phase transition, however, has a unique order parameter which is not particle number density. In this paper, we use unsupervised learning to study the relationship between particle number density, critical point, and latent variables in the site percolation model. It is found that if the input of learning is the original configuration, then the output of unsupervised learning does not convey any information related to the phase transition. Therefore, the maximum cluster is employed in order to effectively capture the critical point of the model. Unsupervised learning yields reliable results consistent with Monte Carlo simulations. We also propose a method called Fake Finite Size Scaling (FFSS) to calculate the critical value, which improves the accuracy of fitting to a great extent.

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Minimalist neural networks training for phase classification in diluted Ising models

Pavioni,

Arlego,

Lamas

2024

Computational Materials Science

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Transfer learning of phase transitions in percolation and directed percolation

Cited by 5 publications

References 33 publications

Supervised and unsupervised learning of (1+1) -dimensional even-offspring branching annihilating random walks

Supervised and unsupervised learning of (1+1) -dimensional even-offspring branching annihilating random walks

Particle density and critical point for studying site percolation by finite size scaling

Minimalist neural networks training for phase classification in diluted Ising models

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