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This study addresses the challenge of predicting network dynamics, such asforecasting disease spread in social networks or estimating species populationsin predator-prey networks. Accurate predictions in large networks are difficultdue to the increasing number of network dynamics parameters that grow with thesize of the network population (e.g., each individual having its own contactand recovery rates in an epidemic process), and because the network topology isunknown or cannot be observed accurately.  Inspired by the low-dimensionality inherent in network dynamics, we propose atwo-step method. First, we decompose the network dynamics into a composite ofprincipal components, each weighted by time-dependent coefficients.Subsequently, we learn the governing differential equations for thesetime-dependent coefficients using sparse regression over a function librarycapable of describing the dynamics. We illustrate the effectiveness of ourproposed approach using simulated network dynamics datasets. The resultsprovide compelling evidence of our method's potential to enhance predictions incomplex networks.

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