Data-driven kernel designs for optimized greedy schemes: A machine learning perspective

T Wenzel, F Marchetti, E Perracchione - SIAM Journal on Scientific Computing, 2024 - SIAM
Thanks to their easy implementation via radial basis functions (RBFs), meshfree kernel
methods have proved to be an effective tool for, eg, scattered data interpolation, PDE …

Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems

H Kleikamp, M Lazar, C Molinari - arXiv preprint arXiv:2307.15590, 2023 - arxiv.org
We consider parametrized linear-quadratic optimal control problems and provide their
online-efficient solutions by combining greedy reduced basis methods and machine …

[HTML][HTML] Greedy kernel methods for approximating breakthrough curves for reactive flow from 3D porous geometry data

R Herkert, P Buchfink, T Wenzel, B Haasdonk… - Mathematics, 2024 - mdpi.com
We address the challenging application of 3D pore scale reactive flow under varying
geometry parameters. The task is to predict time-dependent integral quantities, ie …

[PDF][PDF] Deep and greedy kernel methods: Algorithms, analysis and applications

T Wenzel - 2023 - elib.uni-stuttgart.de
Abstract Machine learning and in particular deep learning techniques are nowadays state of
the art and used in everyday life. Beyond, so-called kernel methods are another class of …

Optimization Problems for PDEs in Weak Space-Time Form

H Harbrecht, A Kunoth, V Simoncini, K Urban - Oberwolfach Reports, 2023 - ems.press
Optimization problems constrained by time-dependent Partial Differential Equations (PDEs)
are challenging from a computational point of view: even in the simplest case, one needs to …