1 citations · 4 across the 7 of their papers we have counts for
9 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…
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 …
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…
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…
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems
Tobias Ehring, Bernard Haasdonk
Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a…