4 papers
Characterization of the reproducing structure of the Bessel potential spaces beyond
Tjeerd Jan Heeringa
Reproducing kernel Hilbert spaces are uniquely characterized by their kernel, but reproducing kernel Banach spaces (RKBS) are not. However, a characterization of which RKBS admit a…
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators
Sven Dummer, Tjeerd Jan Heeringa, José A. Iglesias
Recently, there has been growing interest in characterizing the function spaces underlying neural networks. While shallow and deep scalar-valued neural networks have been linked to…
Deep Networks are Reproducing Kernel Chains
Tjeerd Jan Heeringa, Len Spek, Christoph Brune
Identifying an appropriate function space for deep neural networks remains a key open question. While shallow neural networks are naturally associated with Reproducing Kernel Banac…
Sparsifying dimensionality reduction of PDE solution data with Bregman learning
Tjeerd Jan Heeringa, Christoph Brune, Mengwu Guo
Classical model reduction techniques project the governing equations onto a linear subspace of the original state space. More recent data-driven techniques use neural networks to e…