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Deep Learning of the Biswas-Chatterjee-Sen Model.

José F S Neto1, David S M Alencar1, Lenilson T Brito2

  • 1Departamento de Matemática e Física, Universidade Estadual do Maranhão, Caxias 65604-380, MA, Brazil.

Entropy (Basel, Switzerland)
|November 26, 2025
PubMed
Summary

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Opinion Dynamics Systems on Barabási-Albert Networks: Biswas-Chatterjee-Sen Model.

Entropy (Basel, Switzerland)·2023
This summary is machine-generated.

Deep learning accurately identifies critical points in continuous opinion dynamics. Variational autoencoders reveal phase transitions, with a novel correlation function proving universal at the critical point.

Area of Science:

  • Statistical Physics
  • Computational Physics
  • Machine Learning

Background:

  • Kinetic continuous opinion dynamics models exhibit critical phenomena.
  • Understanding phase transitions in these systems is crucial.
  • Traditional methods for critical point identification can be computationally intensive.

Purpose of the Study:

  • To apply deep learning techniques for analyzing critical properties of kinetic continuous opinion dynamics.
  • To identify the critical point and estimate critical exponents using machine learning.
  • To explore the use of variational autoencoders for phase transition analysis.

Main Methods:

  • Kinetic Monte Carlo simulations to generate spin configuration data.
  • Training dense neural networks to identify critical points on square and triangular lattices.
Keywords:
consensus formationdeep learningkinetic continuous opinion dynamicsnon-equilibrium phase transitionsupervised learningunsupervised learning

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  • Utilizing Principal Component Analysis for magnetization reproduction and critical exponent estimation.
  • Implementing Variational Autoencoders to study phase transitions via the loss function.

    • Main Results:

    • Deep neural networks accurately identified the critical point for the system.
    • Principal Component Analysis successfully reproduced magnetization and estimated critical exponents.
    • The loss function of Variational Autoencoders acted as an order parameter, characterizing the phase transition.
    • A novel correlation function between real and reconstructed data was found to be universal at the critical point.

    Conclusions:

    • Deep learning offers a powerful and accurate approach to studying critical phenomena in complex systems.
    • Variational autoencoders provide a new perspective on phase transitions, with their loss function serving as an order parameter.
    • The universality of the defined correlation function at the critical point suggests broader applicability.