Learning functions, operators and dynamical systems with kernels

Lorenzo Rosasco

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arXiv · 2509.18071

Learning functions, operators and dynamical systems with kernels

Lorenzo Rosasco

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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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Lorenzo Rosasco. 2025-09-22. Learning functions, operators and dynamical systems with kernels. https://arxiv.org/abs/2509.18071

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