Unraveling Low-Dimensional Network Dynamics: A Fusion of Sparse Identification and Proper Orthogonal Decomposition

This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due to the increasing number of network dynamics parameters that grow with the size of the network population (e.g., each individual having its own contact and recovery rates in an epidemic process), and because the network topology is unknown or cannot be observed accurately. Inspired by the low-dimensionality inherent in network dynamics, we propose a two-step method. First, we decompose the network dynamics into a composite of principal components, each weighted by time-dependent coefficients. Subsequently, we learn the governing differential equations for these time-dependent coefficients using sparse regression over a function library capable of describing the dynamics. We illustrate the effectiveness of our proposed approach using simulated network dynamics datasets. The results provide compelling evidence of our method's potential to enhance predictions in complex networks.