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

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.