41 citations · 302 across the 43 of their papers we have counts for
47 papers
Data-driven identification of latent port-Hamiltonian systems
Johannes Rettberg, Jonas Kneifl, Julius Herb +3
Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes…
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…
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…
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…
Port-Hamiltonian Fluid-Structure Interaction Modeling and Structure-Preserving Model Order Reduction of a Classical Guitar
Johannes Rettberg, Dominik Wittwar, Patrick Buchfink +4
A fluid-structure interaction model in a port-Hamiltonian representation is derived for a classical guitar. We combine the laws of continuum mechanics for solids and fluids within…
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…
Surrogate-data-enriched Physics-Aware Neural Networks
Raphael Leiteritz, Patrick Buchfink, Bernard Haasdonk +1
Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss f…
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…
Analysis of Structured Deep Kernel Networks
Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particula…
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…
Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows
Tizian Wenzel, Marius Kurz, Andrea Beck +2
Standard kernel methods for machine learning usually struggle when dealing with large datasets. We review a recently introduced Structured Deep Kernel Network (SDKN) approach that…
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…