True Nonlinear Dynamics from Incomplete Networks

Abstract

We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^{\ast }$. We develop fundamental tools to learn the true steady-state of a small part of the network, without knowing the full network. A naive approach and the current state-of-the-art is to follow the dynamics of the observed partial network to local equilibrium. This dramatically fails to extract the true steady state. We use a mean-field approach to map the dynamics of the unseen part of the network to a single node, which allows us to recover accurate estimates of steady-state on as few as 5 observed vertices in domains ranging from ecology to social networks to gene regulation. Incomplete networks are the norm in practice, and we offer new ways to think about nonlinear dynamics when only sparse information is available.

arXiv commentAAAI 2020, 9 pages, 5 figures

References in corpus (9)

• Epidemic spreading in scale-free networks
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Self-similar community structure in organisations
• Forecast and Control of Epidemics in a Globalized World
• A generalized model of social and biological contagion
• Sampling properties of random graphs: the degree distribution
• Estimating and Sampling Graphs with Multidimensional Random Walks
• Graph Size Estimation
• Counting Motifs with Graph Sampling