Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911957567668224 |
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| author | Evangelou, Nikolaos Giovanis, Dimitrios G. Kevrekidis, George A. Pavliotis, Grigorios A. Kevrekidis, Ioannis G. |
| author_facet | Evangelou, Nikolaos Giovanis, Dimitrios G. Kevrekidis, George A. Pavliotis, Grigorios A. Kevrekidis, Ioannis G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19039 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example Evangelou, Nikolaos Giovanis, Dimitrios G. Kevrekidis, George A. Pavliotis, Grigorios A. Kevrekidis, Ioannis G. Dynamical Systems Machine Learning Multiagent Systems 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. |
| title | Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example |
| topic | Dynamical Systems Machine Learning Multiagent Systems |
| url | https://arxiv.org/abs/2310.19039 |