Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914614829121536 |
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| author | Tian, Moyi Messenger, Daniel A. Dukic, Vanja Rodríguez, Nancy Bortz, David M. |
| author_facet | Tian, Moyi Messenger, Daniel A. Dukic, Vanja Rodríguez, Nancy Bortz, David M. |
| contents | Social systems consist of networks of individuals who influence one another through social interactions. Studying how processes evolve on these networks can help us better understand patterns of social behavior. We study a system that couples online and offline social activity and investigate how to learn effective models directly from data using Weak Form Sparse Identification of Nonlinear Dynamics (WSINDy), a method for discovering governing equations. We assess learning performance using data generated by a mean-field approximation model of a stochastic interaction process on networks and test how accurately the system can be recovered under different noise levels. Our results show that using more trajectories improves accuracy when noise is high, but only a small number of additional trajectories is needed to gain most of the benefit, with little improvement beyond that. We also learn effective ODE models from averaged stochastic data on networks. When traditional mean-field approximations fail, identifying continuum ODEs directly from stochastic processes yields efficient models that better match the data and provide deeper insight into the underlying dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30432 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy Tian, Moyi Messenger, Daniel A. Dukic, Vanja Rodríguez, Nancy Bortz, David M. Dynamical Systems Machine Learning Social and Information Networks Adaptation and Self-Organizing Systems Physics and Society 37N25, 37M10, 62J99, 91D30, 92D30 Social systems consist of networks of individuals who influence one another through social interactions. Studying how processes evolve on these networks can help us better understand patterns of social behavior. We study a system that couples online and offline social activity and investigate how to learn effective models directly from data using Weak Form Sparse Identification of Nonlinear Dynamics (WSINDy), a method for discovering governing equations. We assess learning performance using data generated by a mean-field approximation model of a stochastic interaction process on networks and test how accurately the system can be recovered under different noise levels. Our results show that using more trajectories improves accuracy when noise is high, but only a small number of additional trajectories is needed to gain most of the benefit, with little improvement beyond that. We also learn effective ODE models from averaged stochastic data on networks. When traditional mean-field approximations fail, identifying continuum ODEs directly from stochastic processes yields efficient models that better match the data and provide deeper insight into the underlying dynamics. |
| title | Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy |
| topic | Dynamical Systems Machine Learning Social and Information Networks Adaptation and Self-Organizing Systems Physics and Society 37N25, 37M10, 62J99, 91D30, 92D30 |
| url | https://arxiv.org/abs/2605.30432 |