Unique Reconstruction From Mean-Field Measurements

TL;DR

This paper presents a novel method for reconstructing network structure and dynamics from limited mean-field measurements using localized perturbations and sparse optimization, with proven conditions for unique recovery.

Contribution

It introduces a framework combining perturbations and sparse optimization to achieve unique network reconstruction from aggregated data, addressing a challenging inverse problem.

Findings

Guarantees for unique adjacency matrix recovery

Robustness demonstrated across sparsity regimes

Effective reconstruction of node states and dynamics

Abstract

We address the inverse problem of reconstructing both the structure and dynamics of a network from mean-field measurements, which are linear combinations of node states. This setting arises in applications where only a few aggregated observations are available, making network inference challenging. We focus on the case when the number of mean-field measurements is smaller than the number of nodes. To tackle this ill-posed recovery problem, we propose a framework that combines localized initial perturbations with sparse optimization techniques. We derive sufficient conditions that guarantee the unique reconstruction of the network's adjacency matrix from mean-field data and enable recovery of node states and local governing dynamics. Numerical experiments demonstrate the robustness of our approach across a range of sparsity and connectivity regimes. These results provide theoretical and computational foundations for inferring high-dimensional networked systems from low-dimensional observations.