{"ID":2867874,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.18071","arxiv_id":"2509.18071","title":"Learning functions, operators and dynamical systems with kernels","abstract":"This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning dynamical systems is formulated as a suitable operator learning problem, leveraging Koopman operator theory. The manuscript collects the supporting material for the corresponding course taught at the CIME school \"Machine Learning: From Data to Mathematical Understanding\" in Cetraro.","short_abstract":"This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning dynamical systems is formulated as a suitable operator learning problem, levera...","url_abs":"https://arxiv.org/abs/2509.18071","url_pdf":"https://arxiv.org/pdf/2509.18071v2","authors":"[\"Lorenzo Rosasco\"]","published":"2025-09-22T17:53:08Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}