Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy
This work provides a method for learning effective models of social system dynamics from network data, which is significant for researchers studying social behavior and network processes.
This paper explores learning effective models from network dynamics data using Weak Form Sparse Identification of Nonlinear Dynamics (WSINDy). It demonstrates that increasing the number of trajectories improves model accuracy under high noise, with most benefits achieved with a small number of additional trajectories. The method also successfully learns effective ODE models from averaged stochastic data, outperforming traditional mean-field approximations.
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.