6 papers
Refined rates of convergence for target-data dependent greedy generalized interpolation with Sobolev kernels
Bernard Haasdonk, Gabriele Santin, Tizian Wenzel +1
Greedy methods have recently been successfully applied to generalized kernel interpolation, or the recovery of a function from data stemming from the evaluation of linear functiona…
On the optimal shape parameter for kernel methods: Sharp direct and inverse statements
Tizian Wenzel, Gabriele Santin
The search for the optimal shape parameter for Radial Basis Function (RBF) kernel approximation has been an outstanding research problem for decades. In this work, we establish a t…
Kernel-based Greedy Approximation of Parametric Elliptic Boundary Value Problems
Bernard Haasdonk, Gabriele Santin, Tizian Wenzel
We recently introduced a scale of kernel-based greedy schemes for approximating the solutions of elliptic boundary value problems. The procedure is based on a generalized interpola…
General superconvergence for kernel-based approximation
Toni Karvonen, Gabriele Santin, Tizian Wenzel
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproduc…
Kernel Methods in the Deep Ritz framework: Theory and practice
Hendrik Kleikamp, Tizian Wenzel
In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential…
Greedy Kernel Methods for Approximating Breakthrough Curves for Reactive Flow from 3D Porous Geometry Data
Robin Herkert, Patrick Buchfink, Tizian Wenzel +3
We address the challenging application of 3D pore scale reactive flow under varying geometry parameters. The task is to predict time-dependent integral quantities, i.e., breakthrou…