Hypergraph reconstruction from dynamics

Robin Delabays, Giulia De Pasquale, Florian Dörfler and Yuanzhao Zhang ()
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Robin Delabays: University of Applied Sciences of Western Switzerland HES-SO
Giulia De Pasquale: Eindhoven University of Technology
Florian Dörfler: ETH Zürich
Yuanzhao Zhang: Santa Fe Institute

Nature Communications, 2025, vol. 16, issue 1, 1-9

Abstract: Abstract A plethora of methods have been developed in the past two decades to infer the underlying network structure of an interconnected system from its collective dynamics. However, methods capable of inferring nonpairwise interactions are only starting to appear. Here, we develop an inference algorithm based on sparse identification of nonlinear dynamics (SINDy) to reconstruct hypergraphs and simplicial complexes from time-series data. Our model-free method does not require information about node dynamics or coupling functions, making it applicable to complex systems that do not have a reliable mathematical description. We first benchmark the new method on synthetic data generated from Kuramoto and Lorenz dynamics. We then use it to infer the effective connectivity in the brain from resting-state EEG data, which reveals significant contributions from non-pairwise interactions in shaping the macroscopic brain dynamics.

Date: 2025
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DOI: 10.1038/s41467-025-57664-2

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