Learning the effective order of a hypergraph dynamical system

Science Advances, vol. 10, pp. eadh4053

Abstract

Dynamical systems on hypergraphs can display a rich set of behaviors 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 behavior. 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 a mathematical framework that allows us to determine this order when the type of dynamics is known. We use 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 datasets consisting of observed system trajectories.

Authors 4

1. Leonie Neuhäuser corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Michael Scholkemper corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

3. Francesco Tudisco

   Maxwell Institute for Mathematical Sciences · Gran Sasso Science Institute · University of Edinburgh

   Affiliation as printed

   GSSI Gran Sasso Science Institute, L’Aquila, Italy

   School of Mathematics and Maxwell Institute, University of Edinburgh, Peter Guthrie Tait Road, EH9 3FD, Edinburgh, UK

   GSSI Gran Sasso Science Institute, L'Aquila, Italy

4. Michael T. Schaub corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany