12 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…
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…
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…