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Hypergraph reconstruction from dynamics.

Robin Delabays¹, Giulia De Pasquale², Florian Dörfler³

¹School of Engineering, University of Applied Sciences of Western Switzerland HES-SO, Sion, Switzerland.

Nature Communications

|March 20, 2025

Summary

This summary is machine-generated.

Researchers developed a new method to infer complex network structures, including non-pairwise interactions, from time-series data. This model-free approach reconstructs hypergraphs and simplicial complexes, applicable to systems lacking mathematical descriptions.

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Area of Science:

Complex systems analysis
Network science
Computational neuroscience

Background:

Inferring network structure from dynamics is crucial for understanding complex systems.
Existing methods often struggle with non-pairwise interactions and require detailed system knowledge.
Advanced mathematical models are needed to capture intricate system interdependencies.

Purpose of the Study:

To develop a novel, model-free algorithm for inferring network structures, including higher-order interactions.
To reconstruct complex topologies like hypergraphs and simplicial complexes from time-series data.
To apply the method to real-world data, such as brain activity, to uncover hidden network properties.

Main Methods:

Utilizing sparse identification of nonlinear dynamics (SINDy) for network inference.
Developing an algorithm to reconstruct hypergraphs and simplicial complexes from time-series data.
Benchmarking the method on synthetic data from Kuramoto and Lorenz dynamics.

Main Results:

Successfully reconstructed network structures, including non-pairwise interactions, from synthetic data.
Demonstrated the model-free nature of the algorithm, requiring no prior knowledge of node dynamics or coupling functions.
Applied the method to resting-state electroencephalography (EEG) data to infer effective brain connectivity.

Conclusions:

The developed SINDy-based method effectively infers complex network structures and non-pairwise interactions from time-series data.
This approach offers a powerful tool for analyzing systems without established mathematical models, such as biological networks.
Non-pairwise interactions play a significant role in shaping macroscopic brain dynamics, as revealed by EEG data analysis.