Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example

• URL: http://arxiv.org/abs/2310.19039v2
• Date: Wed, 17 Jul 2024 01:02:50 GMT
• Title: Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example
• Authors: Nikolaos Evangelou, Dimitrios G. Giovanis, George A. Kevrekidis, Grigorios A. Pavliotis, Ioannis G. Kevrekidis,
• Abstract summary: We propose a data-driven framework that pinpoints phase transitions for an agent-based model in its mean-field limit. To this end, we use the manifold learning algorithm Maps to identify a parsimonious set of data-driven latent variables. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deriving closed-form, analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM- the Desai-Zwanzig model in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ODE in these coordinates. We identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE - enabled through an odd symmetry transformation - to construct the bifurcation diagram exhibiting the phase transition.

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