Published In

arXiv preprint

Document Type

Pre-Print

Publication Date

2025

Abstract

We present a representer theorem for a large class of variational problems, generalizing regression, finite element methods, and providing techniques for learning partial and ordinary differential equations (PDEs and ODEs). We apply our formulation to the multivariate occupation kernel method (MOCK) for learning dynamical systems from data. Our generalized method outperforms the MOCK method on most tested datasets, while often requiring considerably fewer parameters. Experiments are presented for learning ODEs and PDEs.

Rights

© Copyright the author(s) 2025

Description

This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published ROCK: Riesz Occupation Kernel Methods for Learning Dynamical Systems. arXiv preprint arXiv:2503.13791.

Persistent Identifier

https://archives.pdx.edu/ds/psu/44295

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