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Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig

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This study introduces a data-driven framework to pinpoint phase transitions in agent-based models (ABMs). It uses manifold learning and deep learning to identify key variables and derive an ODE for analyzing transitions.

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Area of Science:

  • Complex Systems
  • Computational Physics
  • Data Science

Background:

  • Traditional methods for studying phase transitions in agent-based models (ABMs) rely on deriving closed-form analytical expressions for reduced-order models.
  • This approach can be limited by the complexity of choosing appropriate closures and may not always be feasible for intricate systems.

Purpose of the Study:

  • To propose a novel data-driven framework for identifying phase transitions in ABMs, specifically the Desai-Zwanzig model in its mean-field limit.
  • To utilize a reduced set of variables compared to traditional closed-form models for more efficient analysis.
  • To demonstrate the framework's ability to construct a bifurcation diagram exhibiting phase transitions.

Main Methods:

  • Application of the Diffusion Maps manifold learning algorithm to identify a parsimonious set of data-driven latent variables.
  • Utilizing a deep learning framework for conformal reparametrization of these latent variables.
  • Identification of a parameter-dependent ordinary differential equation (ODE) using a residual neural network inspired by the forward Euler integration scheme.

Main Results:

  • The identified data-driven latent variables were shown to be in one-to-one correspondence with the theoretical order parameter of the ABM.
  • A single ODE was successfully derived in the reparametrized coordinates, facilitating the analysis.
  • The derived ODE, combined with an odd symmetry transformation, enabled the construction of a bifurcation diagram that clearly exhibits the phase transition.

Conclusions:

  • The proposed data-driven framework offers an effective alternative to traditional analytical methods for studying phase transitions in ABMs.
  • This approach allows for the analysis of complex systems using a smaller, data-identified set of variables.
  • The successful construction of the bifurcation diagram validates the framework's capability in pinpointing critical transitions.