Clustering in co-evolving opinion dynamics: reduced SPDE models
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910180688527360 |
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| author | Zimper, Sebastian Conrad, Nataša Djurdjevac Cornalba, Federico Djurdjevac, Ana |
| author_facet | Zimper, Sebastian Conrad, Nataša Djurdjevac Cornalba, Federico Djurdjevac, Ana |
| contents | Clustering is a fundamental collective phenomenon in agent-based models (ABMs) of opinion dynamics. To study clustering in systems with co-evolving social and opinion variables, we derive stochastic partial differential equation (SPDE) models that describe the evolution of clusters on a reduced state space. We consider two settings: one in which opinions do not affect social interactions, and another one in which a feedback mechanism couples the two. Our approach extends reduced PDE modelling to a stochastic framework, which is essential for capturing long-term cluster behaviour. Numerical experiments demonstrate that the proposed reduced SPDEs substantially decrease computational cost compared to full-state SPDE models, such as the Dean-Kawasaki equation, while still accurately reproducing the clustering behaviour of the underlying ABM. As a result, these reduced models provide an efficient tool for studying systems with large populations, including those arising in the analysis of real-world data: in particular, we provide an application related to the large-scale General Social Survey (GSS), which comprises opinion and social data of the US population since 1972. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27961 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Clustering in co-evolving opinion dynamics: reduced SPDE models Zimper, Sebastian Conrad, Nataša Djurdjevac Cornalba, Federico Djurdjevac, Ana Physics and Society Dynamical Systems Probability Clustering is a fundamental collective phenomenon in agent-based models (ABMs) of opinion dynamics. To study clustering in systems with co-evolving social and opinion variables, we derive stochastic partial differential equation (SPDE) models that describe the evolution of clusters on a reduced state space. We consider two settings: one in which opinions do not affect social interactions, and another one in which a feedback mechanism couples the two. Our approach extends reduced PDE modelling to a stochastic framework, which is essential for capturing long-term cluster behaviour. Numerical experiments demonstrate that the proposed reduced SPDEs substantially decrease computational cost compared to full-state SPDE models, such as the Dean-Kawasaki equation, while still accurately reproducing the clustering behaviour of the underlying ABM. As a result, these reduced models provide an efficient tool for studying systems with large populations, including those arising in the analysis of real-world data: in particular, we provide an application related to the large-scale General Social Survey (GSS), which comprises opinion and social data of the US population since 1972. |
| title | Clustering in co-evolving opinion dynamics: reduced SPDE models |
| topic | Physics and Society Dynamical Systems Probability |
| url | https://arxiv.org/abs/2604.27961 |