Dynamical networks reconstructed from time series

TL;DR

This paper introduces a new method for reconstructing dynamical networks from time series data by analyzing variable-derivative correlations, enabling direct derivation of the network's adjacency matrix.

Contribution

The paper presents a novel, straightforward approach to network reconstruction that leverages variable-derivative correlations, applicable to any network type with known interaction functions.

Findings

Method successfully reconstructs network adjacency matrices from time series.

Reconstruction accuracy depends on properties of the time series.

Errors in reconstruction can be estimated and minimized.

Abstract

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency matrix, assuming the intra-network interaction functions to be known. We illustrate the method on a simple example, and discuss the dependence of the reconstruction precision on the properties of time series. Our method is applicable to any network, allowing for reconstruction precision to be maximized, and errors to be estimated.