aiqbench analysis
This research demonstrates that Weak Form Sparse Identification of Nonlinear Dynamics (WSINDy) can effectively recover governing equations from noisy network data, outperforming traditional mean-field approximations in stochastic environments. The study highlights a key efficiency gain where accuracy plateaus after adding a small number of trajectories, suggesting diminishing returns for further data collection in high-noise regimes. By identifying continuum ODEs directly from stochastic processes, the method offers a robust approach for modeling complex social systems where standard approximations fail.
Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy
arXiv:2605.30432v2 Announce Type: replace-cross Abstract: 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.
Abstract: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.
24 pages, 14 figures, 1 table. Code available at this https URL
Dynamical Systems (math.DS); Machine Learning (cs.LG); Social and Information Networks (cs.SI); Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph)
arXiv:2605.30432 [math.DS]
(or arXiv:2605.30432v2 [math.DS] for this version)
Full text under the publisher's open licence · 212 words
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