Reconstruction of noise-driven nonlinear networks from node outputs by using high-order correlations

Area of Science:

• Complex Systems Science
• Network Science
• Data Analysis

Background:

• Practical systems generate rich data, but their underlying network structures remain hidden.
• Existing methods often struggle to simultaneously address network nonlinearity and noise.

Purpose of the Study:

• To develop a unified framework for inferring dynamic nonlinearities, topological links, and noise structures in complex networks.
• To address the limitations of current network reconstruction techniques by considering both nonlinearity and noise.

Main Methods:

• Utilizing high-order correlation computations (HOCC) to model nonlinear dynamics.
• Employing two-time correlations to distinguish network dynamics from noise.
• Developing suitable basis and correlator vectors for unified inference.

Main Results:

• A closed-form theoretical framework for network structure inference.
• Successful numerical simulations validating the theoretical predictions.
• Unified inference of nonlinearities, interactions, and noise statistics.

Conclusions:

• The proposed HOCC-based framework provides a robust solution for reconstructing complex dynamic networks.
• This method effectively handles both nonlinear dynamics and inherent system noise.
• The findings offer significant advancements in understanding and modeling real-world systems.