Jianyu Hu: A Global Structure-Preserving Kernel Method for the Learning of Poisson Systems
Автор: Machine Learning and Dynamical Systems Seminar
Загружено: 2025-06-05
Просмотров: 76
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Day: 05 June 2025
Speaker: Jianyu Hu
Title: A Global Structure-Preserving Kernel Method for the Learning of Poisson Systems
Abstract: A structure-preserving kernel ridge regression method is presented that allows the recovery of globally defined, potentially high-dimensional, and nonlinear Hamiltonian functions on Poisson manifolds out of datasets made of noisy observations of Hamiltonian vector fields. The proposed method is based on finding the solution of a non-standard kernel ridge regression where the observed data is generated as the noisy image by a vector bundle map of the differential of the function that one is trying to estimate. Additionally, it is shown how a suitable regularization solves the intrinsic non-identifiability of the learning problem due to the degeneracy of the Poisson tensor and the presence of Casimir functions. A full error analysis is conducted that provides convergence rates using fixed and adaptive regularization parameters. The good performance of the proposed estimator is illustrated with several numerical experiments.
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