Learning the effective order of a hypergraph dynamical system

arXiv (Cornell University)

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.

Authors 4

1. Leonie Neuhäuser
2. Michael Scholkemper Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Aachen , Germany

3. Francesco Tudisco

   Gran Sasso Science Institute

   Affiliation as printed

   GSSI Gran Sasso Science Institute , L'Aquila , Italy

4. Michael T. Schaub Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Aachen , Germany