Machine learning for the identification of phase transitions in interacting agent-based systems: a Desai-Zwanzig example
File(s)
Accepted version
Author(s)
Evangelou, Nikolaos
Giovanis, Dimitris G
Kevrekidis, George A
Pavliotis, Grigorios A
Kevrekidis, Ioannis G
Type
Journal Article
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 we 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 ordinary differential equation (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.
Date Issued
2024-07
Date Acceptance
2024-06-17
Citation
Physical Review E, 2024, 110 (1)
ISSN
2470-0045
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
110
Issue
1
Copyright Statement
Copyright © 2024 American Physical Society. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Identifier
http://dx.doi.org/10.1103/physreve.110.014121
Publication Status
Published
Article Number
014121
Date Publish Online
2024-07-15