Learning functions, operators and dynamical systems with kernels

Lorenzo Rosasco
9/22/2025
cs.LG

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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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Cite this paper

@article{rosasco2025learning,
  title  = {Learning functions, operators and dynamical systems with kernels},
  author = {Lorenzo Rosasco},
  year   = {2025},
  eprint = {2509.18071},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2509.18071v2}
}

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