Learning Models from Network Dynamics Data using Weak Form SINDy

Learning the mechanisms of network dynamics from data is useful, as in social systems, agents are often connected and interact through networks. We focus on the online-offline coupled system of social activities and study how we can learn effective models from data using Weak Form Sparse Identification of Nonlinear Dynamics (WSINDy), a system discovery method. We first test learning performance using data generated by the fully-mixed mean-field approximation model and examine the accuracy of system recovery at different noise levels. Surprisingly, adding minimal additional trajectory information leads to significant improvement in learning accuracy in the presence of more noise. We then focus on learning effective ODE models from averaged stochastic data on networks. Our results suggest that using more trajectories can improve learning in certain cases. One highlight of identifying continuum ODEs from stochastic processes is that it can provide efficient models that closely match the data, especially when traditional mean-field approximations fail. In such situations, the learned models serve as better approximations, providing deeper insights into the underlying mechanisms.