Moyi Tian, Department of Applied Mathematics, University of Colorado Boulder

Modeling and Learning Dynamics of Online–Offline Social Systems on Networks

Social media increasingly transforms offline life, from everyday decisions to the escalation of conflicts, while offline events in turn drive online discussion and engagement. To understand these interrelated influences, it is crucial to establish models that capture the coupled dynamics and methods that can learn such mechanisms from data. We present initial efforts along two complementary directions. First, motivated by the high activity and wide influence of bots on the internet, we use multi-agent large language model (LLM) simulations on networks to generate dynamics of online information spread tied to real events, assigning agents different personalities to trigger diverse behaviors. By fitting these data to mathematical models, we find that mean-field approximations provide an effective framework for capturing the dynamics. This motivates our second line of work, where we explore data-driven system identification. In particular, we present preliminary results using Weak SINDy to recover continuum models from synthetic engagement data. Together, these approaches illustrate early steps toward bridging simulation, modeling, and data-driven learning for online–offline social systems.