Recovering sparse networks: Basis adaptation and stability under extensions.

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 technique. 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. • Recovering network structure by least squares techniques can be unstable. • Ergodicity of the underlying dynamical system induces a set of adapted basis functions. • Sparse recovery method is stable when the set of adapted basis functions is used. [ABSTRACT FROM AUTHOR]