Learning functions, operators and dynamical systems with kernels
- URL: http://arxiv.org/abs/2509.18071v2
- Date: Tue, 23 Sep 2025 13:43:42 GMT
- Title: Learning functions, operators and dynamical systems with kernels
- Authors: Lorenzo Rosasco,
- Abstract summary: The basic framework is introduced for scalar-valued learning and then extended to operator learning.<n>Learning dynamical systems is formulated as a suitable operator learning problem, leveraging Koopman operator theory.
- Score: 10.386111670902816
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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