Recovering sparse networks: Basis adaptation and stability under extensions

Abstract

We consider the problem of recovering equations of motion from multivariate time series of oscillators interacting on sparse networks. We reconstruct the network from an initial guess which can include expert knowledge about the system such as main motifs and hubs. When sparsity is taken into account the number of data points needed is drastically reduced when compared to the least-squares recovery. We show that the sparse solution is stable under basis extensions, that is, once the correct network topology is obtained, the result does not change if further motifs are considered.

22 pages, 5 figure

References in corpus (4)

• Revealing Network Connectivity From Dynamics
• Coupling functions: Universal insights into dynamical interaction mechanisms
• Learning dynamical systems from data: a simple cross-validation perspective
• Reconstruction of a random phase dynamics network from observations

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