Hypergraph reconstruction from dynamics

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.