1 citations · 4 across the 11 of their papers we have counts for
13 papers
On Symmetric Kernel Collocation for Nonlinear PDEs
Milan Bacchetta, Tobias Ehring, Bernard Haasdonk
This paper considers kernel-based approximation methods for nonlinear partial differential equations. To this end, the problem is formulated as an optimal-recovery generalized inte…
Symplecticity-preserving prediction of parameter-dependent Hamiltonian dynamics by Generalized Kernel Interpolation
Robin Herkert, Tobias Ehring, Bernard Haasdonk
We extend the kernel-based symplectic predictor of [1] to a parameter-augmented setting in which the learned flow-map surrogate depends not only on the state, but also on additiona…
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…
Symplecticity-Preserving Prediction of Hamiltonian Dynamics by Generalized Kernel Interpolation
Robin Herkert, Tobias Ehring, Bernard Haasdonk
In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method lea…
Recovery of the optimal control value function in reproducing kernel Hilbert spaces from verification conditions
Tobias Ehring, Behzad Azmi, Bernard Haasdonk
Approximating the optimal value function for infinite-horizon, nonlinear, autonomous optimal control problems is both challenging and essential for synthesizing real-time opt…
Escaping the native space of Sobolev kernels by interpolation
Tobias Ehring, Max-Paul Vogel, Bernard Haasdonk
Classical convergence analysis for kernel interpolation typically assumes that the target function lies in the reproducing kernel Hilbert space …
Convergence Rates for Realizations of Gaussian Random Variables
Daniel Winkle, Ingo Steinwart, Bernard Haasdonk
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables…
Solving Approximation Tasks with Greedy Deep Kernel Methods
Marian Klink, Tobias Ehring, Robin Herkert +3
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inhere…
On the Convergence of the Policy Iteration for Infinite-Horizon Nonlinear Optimal Control Problems
Tobias Ehring, Behzad Azmi, Bernard Haasdonk
Policy iteration (PI) is a widely used algorithm for synthesizing optimal feedback control policies across many engineering and scientific applications. When PI is deployed on infi…
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…
A trust-region framework for optimization using Hermite kernel surrogate models
Sven Ullmann, Tobias Ehring, Robin Herkert +1
In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding…
Convergence Analysis of a Greedy Algorithm for Conditioning Gaussian Random Variables
Daniel Winkle, Ingo Steinwart, Bernard Haasdonk
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergenc…
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…