A Structure-Preserving Kernel Method for Learning Hamiltonian Systems

arXiv:2403.10070v1 Announce Type: cross
Abstract: A structure-preserving kernel ridge regression method is presented that allows the recovery of potentially high-dimensional and nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form solution that yields excellent numerical performances that surpass other techniques proposed in the literature in this setup. From the methodological point of view, the paper extends kernel regression methods to problems in which loss functions involving linear functions of gradients …

abstract arxiv cs.lg datasets fields form functions kernel math.ds numerical performances recovery regression ridge solution stat.ml systems type vector