# Learning functions, operators and dynamical systems with kernels

arXiv: https://arxiv.org/abs/2509.18071 · HTML: https://mlsanity.com/paper/2509.18071/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 3 of 3)

- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)

## Abstract (arXiv)

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.