{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/machine-learning-for-the-identification-of","title":"Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example","arxiv_id":"2310.19039","date":"2023-10-29","proceeding":null,"authors":["Nikolaos Evangelou","Dimitrios G. Giovanis","George A. Kevrekidis","Grigorios A. Pavliotis","Ioannis G. Kevrekidis"],"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.","url_abs":"https://arxiv.org/abs/2310.19039v2","url_pdf":"https://arxiv.org/pdf/2310.19039v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"machine-learning-for-the-identification-of","repo_url":"https://gitlab.com/nicolasevangelou/ml_phase_transition","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"numerical-integration","task_name":"Numerical Integration"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"},{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}