Hypergraph reconstruction from dynamics

TL;DR

This paper introduces a novel, model-free algorithm based on SINDy for reconstructing hypergraphs and simplicial complexes from time-series data, capable of identifying nonpairwise interactions in complex systems.

Contribution

It presents the first SINDy-based method for hypergraph inference that does not require prior knowledge of node dynamics or coupling functions.

Findings

Successfully benchmarked on synthetic Kuramoto and Lorenz data.

Revealed significant non-pairwise interactions in brain EEG data.

Demonstrated applicability to complex, real-world systems.

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.