  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.
