Learning the effective order of a hypergraph dynamical system

TL;DR

This paper introduces a method to identify the minimal hypergraph order needed to accurately replicate complex dynamical systems, combining analytical techniques with hypergraph neural networks on synthetic and real data.

Contribution

It presents a novel analytical framework and neural network approach to determine the necessary hypergraph order for modeling dynamical systems.

Findings

Successfully determines hypergraph order from observed data

Applies method to synthetic and real-world datasets

Enhances understanding of hypergraph structure in dynamics

Abstract

Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to faithfully replicate the observed dynamical behaviour. To answer this question, we propose a method to determine the minimum order of a hypergraph necessary to approximate the corresponding dynamics accurately. Specifically, we develop an analytical framework that allows us to determine this order when the type of dynamics is known. We utilize these ideas in conjunction with a hypergraph neural network to directly learn the dynamics itself and the resulting order of the hypergraph from both synthetic and real data sets consisting of observed system trajectories.