2021/01/30 by Mauro Maggioni, Maggioni, Mauro, Jason Miller +5 · 4 citations
Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Opinion Dynamics and Social Influence #Quantum chaos and dynamical systems #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2102.00327
openalex publication_date 2021/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering. We consider the problem of learning interaction kernels in these dynamical systems constrained to evolve on Riemannian manifolds from given trajectory data. The models we consider are based on interaction kernels depending on pairwise Riemannian distances between agents, with agents interacting locally along the direction of the shortest geodesic connecting them. We show that our estimators converge at a rate that is independent of the dimension of the state space, and derive bounds on the trajectory estimation error, on the manifold, between the observed and estimated dynamics. We demonstrate the performance of our estimator on two classical first order interacting systems: Opinion Dynamics and a Predator-Swarm system, with each system constrained on two prototypical manifolds, the 2-dimensional sphere and the Poincaré disk model of hyperbolic space.