Robust reconstruction of sparse network dynamics
File(s)
Published version
Author(s)
Pereira, Tiago
Roque Dos Santos, Edmilson
van Strien, Sebastian
Type
Journal Article
Abstract
Reconstructing the network interaction structure from multivariate time series is an important problem in multiple fields of science. When the network dynamics is represented as a linear combination of multivariate polynomials, the reconstruction can be formulated as an optimisation problem. For large networks, this optimisation problem does not always have a unique solution, leading to wrong reconstruction. We propose the Ergodic Basis Pursuit (EBP) method, which leverages the statistical properties of the network dynamics to accurately reconstruct sparse networks. The key idea is that the restricted isometry property of the associated library matrix—a crucial condition for ensuring unique reconstruction—can be derived from the ergodic properties of the network dynamics. We show that when the data length scales quadratically with node degree and logarithmically with network size the reconstruction is unique. Compared to traditional methods, the EBP reconstructs sparse networks using significantly less data and is robust to noise. We validate its effectiveness using experimental time series from optoelectronic networks.
Date Issued
2025-05-15
Date Acceptance
2025-05-02
Citation
Nonlinearity, 2025, 38 (5)
ISSN
0951-7715
Publisher
IOP Publishing
Journal / Book Title
Nonlinearity
Volume
38
Issue
5
Copyright Statement
© 2025 The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Identifier
10.1088/1361-6544/add3b0
Publication Status
Published
Article Number
ARTN 055031
Date Publish Online
2025-05-15