Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy

2026-05-28

AI Summary

This work addresses the failure of traditional mean-field approximations in modeling social behavior dynamics under high-noise networked settings by proposing a method based on the weak-form sparse identification of nonlinear dynamics (WSINDy). The approach directly learns continuous-time ordinary differential equation models from noisy trajectory data collected under multiple initial conditions, capturing the evolution of online-offline coupled social behaviors without relying on mean-field assumptions. By leveraging the weak formulation, the method recovers high-fidelity, interpretable dynamical models directly from stochastic process data. Experimental results demonstrate that incorporating only a few additional initial conditions substantially improves modeling accuracy in high-noise environments, significantly outperforming conventional mean-field approaches.

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.

Problem

• network dynamics
• social systems
• stochastic processes
• mean-field approximation
• model learning

Innovation

• WSINDy
• network dynamics
• mean-field approximation
• stochastic processes
• ODE discovery