41 citations · 302 across the 43 of their papers we have counts for
32 papers · 1 filter
Error Analysis of Randomized Symplectic Model Order Reduction for Hamiltonian systems
Robin Herkert, Patrick Buchfink, Bernard Haasdonk +2
Solving high-dimensional dynamical systems in multi-query or real-time applications requires efficient surrogate modelling techniques, as e.g., achieved via model order reduction (…
Model reduction on manifolds: A differential geometric framework
Patrick Buchfink, Silke Glas, Bernard Haasdonk +1
Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric f…
Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds
Patrick Buchfink, Silke Glas, Bernard Haasdonk
For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov n-width describes the best-possible error for a reduced order model (ROM) of…
On the optimality of target-data-dependent kernel greedy interpolation in Sobolev Reproducing Kernel Hilbert Spaces
Gabriele Santin, Tizian Wenzel, Bernard Haasdonk
Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to cer…
Dictionary-based Online-adaptive Structure-preserving Model Order Reduction for Parametric Hamiltonian Systems
Robin Herkert, Patrick Buchfink, Bernard Haasdonk
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems wi…
Improved a posteriori Error Bounds for Reduced port-Hamiltonian Systems
Johannes Rettberg, Dominik Wittwar, Patrick Buchfink +3
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error c…
Randomized Symplectic Model Order Reduction for Hamiltonian Systems
Robin Herkert, Patrick Buchfink, Bernard Haasdonk +2
Simulations of large scale dynamical systems in multi-query or real-time contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction (MOR)…
Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling
Tizian Wenzel, Bernard Haasdonk, Hendrik Kleikamp +2
In the framework of reduced basis methods, we recently introduced a new certified hierarchical and adaptive surrogate model, which can be used for efficient approximation of input-…
Adaptive meshfree approximation for linear elliptic partial differential equations with PDE-greedy kernel methods
Tizian Wenzel, Daniel Winkle, Gabriele Santin +1
We consider meshless approximation for solutions of boundary value problems (BVPs) of elliptic Partial Differential Equations (PDEs) via symmetric kernel collocation. We discuss th…
A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs
B. Haasdonk, H. Kleikamp, M. Ohlberger +2
We present a new surrogate modeling technique for efficient approximation of input-output maps governed by parametrized PDEs. The model is hierarchical as it is built on a full ord…
Stability of convergence rates: Kernel interpolation on non-Lipschitz domains
Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces (RKHS) usually assume quite restrictive properties on the shape of the domain, especially in the case…
Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds
Patrick Buchfink, Silke Glas, Bernard Haasdonk
Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. For problems with slowly decaying Kolmogorov-n-width…
An adaptive model hierarchy for data-augmented training of kernel models for reactive flow
Bernard Haasdonk, Mario Ohlberger, Felix Schindler
We consider machine-learning of time-dependent quantities of interest derived from solution trajectories of parabolic partial differential equations. For large-scale or long-time i…
Analysis of target data-dependent greedy kernel algorithms: Convergence rates for -, - and -greedy
Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
Data-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this expe…
A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows
Pavel Gavrilenko, Bernard Haasdonk, Oleg Iliev +5
We present an integrated approach for the use of simulated data from full order discretization as well as projection-based Reduced Basis reduced order models for the training of ma…
Reduced Basis Methods for Efficient Simulation of a Rigid Robot Hand Interacting with Soft Tissue
Shahnewaz Shuva, Patrick Buchfink, Oliver Röhrle +1
We present efficient reduced basis (RB) methods for the simulation of the coupled problem consisting of a rigid robot hand interacting with soft tissue material which is modeled by…
Kernel methods for center manifold approximation and a data-based version of the Center Manifold Theorem
Bernard Haasdonk, Boumediene Hamzi, Gabriele Santin +1
For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows…
Biomechanical surrogate modelling using stabilized vectorial greedy kernel methods
Bernard Haasdonk, Tizian Wenzel, Gabriele Santin +1
Greedy kernel approximation algorithms are successful techniques for sparse and accurate data-based modelling and function approximation. Based on a recent idea of stabilization of…
Sampling based approximation of linear functionals in Reproducing Kernel Hilbert Spaces
Gabriele Santin, Toni Karvonen, Bernard Haasdonk
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature r…
A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability & uniform point distribution
Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ing…
Kernel Methods for Surrogate Modeling
Gabriele Santin, Bernard Haasdonk
This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition…
Symplectic Model Order Reduction with Non-Orthonormal Bases
Patrick Buchfink, Ashish Bhatt, Bernard Haasdonk
Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a re…
Greedy regularized kernel interpolation
Gabriele Santin, Dominik Wittwar, Bernard Haasdonk
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding functi…
Interpolation with uncoupled separable matrix-valued kernels
Dominik Wittwar, Gabriele Santin, Bernard Haasdonk
In this paper we consider the problem of approximating vector-valued functions over a domain . For this purpose, we use matrix-valued reproducing kernels, which can be related t…