Reconstruction of network dynamics from partial observations

TL;DR

This paper explores how to reconstruct network node time series from partial, noisy observations, analyzing linear and nonlinear dynamics, and introduces a computational method for reconstruction.

Contribution

It introduces the observation error magnification factor (OEMF) for assessing noise impact and presents a new computational approach for partial network time series reconstruction.

Findings

OEMF quantifies noise amplification in reconstruction

Comparison of OEMF aids optimal network observation strategies

Proposed method effectively reconstructs time series from partial data

Abstract

We investigate the reconstruction of time series from dynamical networks that are partially observed. In particular, we address the extent to which the time series at a node of the network can be successfully reconstructed when measuring from another node, or subset of nodes, corrupted by observational noise. We will assume the dynamical equations of the network are known, and that the dynamics are not necessarily low-dimensional. The case of linear dynamics is treated first, and leads to a definition of observation error magnification factor (OEMF) that measures the magnification of noise in the reconstruction process. Subsequently, the definition is applied to nonlinear and chaotic dynamics. Comparison of OEMF for different target/observer combinations can lead to better understanding of how to optimally observe a network. As part of the study, a computational method for reconstructing time series from partial observations is presented and analyzed.