A Reconstruction algorithm for an unknown network

TL;DR

This paper introduces a Wiener filtering-based reconstruction algorithm that detects links in dynamical systems networks, providing theoretical guarantees and conditions for accurate link detection in various network classes.

Contribution

The paper presents a novel reconstruction method with theoretical guarantees for link detection in dynamical networks, including conditions for networks outside the self-kin class.

Findings

Provides conditions for correct link detection in self-kin networks

Extends detection guarantees to networks within the smallest self-kin network containing the true network

Offers a general theoretical framework for network reconstruction

Abstract

The interest for networks of dynamical systems has been increasing in the past years, especially because of their capability of modeling and describing a large variety of phenomena and behaviors. We propose a technique, based on Wiener filtering, which provides general theoretical guarantees for the detection of links in a network of dynamical systems. For a large class of network that we name "self-kin" sufficient conditions for a correct detection of a link are formulated. For networks not belonging to this class we give conditions for correct detection of links belonging to the smallest self-kin network containing the actual one.