# Reconstructing propagation networks with natural diversity and identifying hidden sources

arXiv: https://arxiv.org/abs/1407.4451 · HTML: https://mlsanity.com/paper/1407.4451/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2014.

## Built on by (most cited first, 5 of 5)

- [Data-driven model discovery with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2409.15167/) (2024)
- [Unsupervised learning for anticipating critical transitions](https://mlsanity.com/paper/2501.01579/) (2025)
- [Digital twins of nonlinear dynamical systems: A perspective](https://mlsanity.com/paper/2309.11461/) (2023)
- [A Bayesian Approach for the Network Reconstruction of Interdependent Critical Infrastructure Systems from Cascading Failures](https://mlsanity.com/paper/2211.15590/) (2022)
- [Machine learning of network inference enhancement from noisy measurements](https://mlsanity.com/paper/2309.02050/) (2023)

## Abstract (arXiv)

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.