2023/06/02 by Leonie Neuhäuser, Michael Scholkemper, Neuhäuser, Leonie +5 · 3 citations
Computer Science · #Computational Physics and Python Applications #Data Visualization and Analytics #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2306.01813
openalex publication_date 2023/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.