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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.
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