Decoupling approximation robustly reconstructs directed dynamical networks

TL;DR

This paper introduces a decoupling approximation method for reconstructing directed dynamical networks from time-series data, which is computationally efficient, assumption-free, and robust to noise and data limitations.

Contribution

The paper presents a novel decoupling approximation approach that significantly reduces computational costs while maintaining high reconstruction accuracy in directed dynamical networks.

Findings

Performance close to ideal exhaustive methods

Highly robust to noise and data limitations

Independent of dynamical regimes

Abstract

Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about properties of the dynamics, and can cope with noisy, short and incomplete trajectories. Ideal reconstruction in such scenario requires and exhaustive approach of simulating the dynamics for all possible network configurations and matching the simulated against the actual trajectories, which of course is computationally too costly for any realistic application. Relying on insights from equation discovery and machine learning, we here introduce \textit{decoupling approximation} of dynamical networks and propose a new reconstruction method based on it. Decoupling approximation consists of matching the simulated against the actual trajectories for each node individually rather than for the entire network at once. Despite drastic reduction of the computational cost that this approximation entails, we find our method's performance to be very close to that of the ideal method. In particular, we not only make no assumptions about properties of the trajectories, but provide strong evidence that our methods' performance is largely independent of the dynamical regime at hand. Of crucial relevance for practical applications, we also find our method to be extremely robust to both length and resolution of the trajectories and relatively insensitive to noise.