Recovering sparse networks: Basis adaptation and stability under extensions

TL;DR

This paper presents a method for recovering sparse networks of oscillators from time series data, demonstrating that incorporating sparsity reduces data requirements and that the recovered network remains stable under basis extensions.

Contribution

It introduces a basis adaptation approach for sparse network recovery that is stable under extensions, improving robustness and efficiency over traditional methods.

Findings

Sparsity reduces data needed for accurate network recovery.

Recovered networks are stable under basis extensions.

Method outperforms least-squares in sparse settings.

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.