  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.
