Bernard Haasdonk
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View article: Data-driven identification of latent port-Hamiltonian systems
Data-driven identification of latent port-Hamiltonian systems Open
View article: Error analysis of randomized symplectic model order reduction for Hamiltonian systems
Error analysis of randomized symplectic model order reduction for Hamiltonian systems Open
View article: Convergence Rates for Realizations of Gaussian Random Variables
Convergence Rates for Realizations of Gaussian Random Variables Open
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 using finitely many observations. We derive non-asymptotic …
View article: Kernel-based Greedy Approximation of Parametric Elliptic Boundary Value Problems
Kernel-based Greedy Approximation of Parametric Elliptic Boundary Value Problems Open
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 interpolation framework in reproducing kernel Hilbert spaces and was…
View article: Convergence Analysis of a Greedy Algorithm for Conditioning Gaussian Random Variables
Convergence Analysis of a Greedy Algorithm for Conditioning Gaussian Random Variables Open
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables remai…
View article: Online adaptive surrogates for the value function of high-dimensional nonlinear optimal control problems
Online adaptive surrogates for the value function of high-dimensional nonlinear optimal control problems Open
View article: Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds
Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds Open
For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov -width describes the best-possible error for a reduced order model (ROM) of size . In this paper, we provide approximation bounds for RO…
View article: Improved a posteriori error bounds for reduced port-Hamiltonian systems
Improved a posteriori error bounds for reduced port-Hamiltonian systems Open
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 can be bounded by residual-based methods, which are typicall…
View article: Data-driven identification of latent port-Hamiltonian systems
Data-driven identification of latent port-Hamiltonian systems Open
Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven sy…
View article: Model reduction on manifolds: A differential geometric framework
Model reduction on manifolds: A differential geometric framework Open
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 framework for model reduction on smooth manifolds, which emp…
View article: Greedy Kernel Methods for Approximating Breakthrough Curves for Reactive Flow from 3D Porous Geometry Data
Greedy Kernel Methods for Approximating Breakthrough Curves for Reactive Flow from 3D Porous Geometry Data Open
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., breakthrough curves, from the given geometries. As the 3D reactive fl…
View article: Greedy Kernel Methods for Approximating Breakthrough Curves for Reactive Flow from 3D Porous Geometry Data
Greedy Kernel Methods for Approximating Breakthrough Curves for Reactive Flow from 3D Porous Geometry Data Open
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., breakthrough curves, from the given geometries. As the 3D reactive fl…
View article: Inhalt: Chem. Ing. Tech. 6/2024
Inhalt: Chem. Ing. Tech. 6/2024 Open
study demonstrates the potential for using compartment models with creeping flow, providing scalable and accurate results across multiple points.. . . . . . . . . .
View article: Error Analysis of Randomized Symplectic Model Order Reduction for Hamiltonian systems
Error Analysis of Randomized Symplectic Model Order Reduction for Hamiltonian systems Open
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 (MOR). If these systems are Hamiltonian systems their physic…
View article: Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems Open
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 mesh-free data-based approximation method for the value fu…
View article: Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems
Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems Open
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n -widths. Additionally, Hami…
View article: Goal‐Oriented Two‐Layered Kernel Models as Automated Surrogates for Surface Kinetics in Reactor Simulations
Goal‐Oriented Two‐Layered Kernel Models as Automated Surrogates for Surface Kinetics in Reactor Simulations Open
Multi‐scale modeling allows the description of real reactive systems under industrially relevant conditions. However, its application to rational catalyst and reactor design is hindered by the prohibitively high computational cost associat…
View article: A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs
A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs Open
View article: Model reduction on manifolds: A differential geometric framework
Model reduction on manifolds: A differential geometric framework Open
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 framework for model reduction on smooth manifolds, which emp…
View article: Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds
Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds Open
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 size n. In this paper, we provide approximation bounds for …
View article: Improving Determination of Pigment Contents in Microalgae Suspension with Absorption Spectroscopy: Light Scattering Effect and Bouguer–Lambert–Beer Law
Improving Determination of Pigment Contents in Microalgae Suspension with Absorption Spectroscopy: Light Scattering Effect and Bouguer–Lambert–Beer Law Open
The Bouguer–Lambert–Beer (BLB) law serves as the fundamental basis for the spectrophotometric determination of pigment content in microalgae. Although it has been observed that the applicability of the BLB law is compromised by the light s…
View article: On the optimality of target-data-dependent kernel greedy interpolation in Sobolev Reproducing Kernel Hilbert Spaces
On the optimality of target-data-dependent kernel greedy interpolation in Sobolev Reproducing Kernel Hilbert Spaces Open
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 certain Sobolev spaces. In the context of interpolation, the s…
View article: Designing energy-conserving surrogate models for the coupled,non-linear responses of intervertebral discs
Designing energy-conserving surrogate models for the coupled,non-linear responses of intervertebral discs Open
The aim of this study was to design physics-preserving and precise surrogate models of the non-linear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) dis…
View article: Port-Hamiltonian fluid–structure interaction modelling and structure-preserving model order reduction of a classical guitar
Port-Hamiltonian fluid–structure interaction modelling and structure-preserving model order reduction of a classical guitar Open
A fluid–structure interaction model in a port-Hamiltonian representation is derived for a classical guitar. After discretization, we combine the laws of continuum mechanics for solids and fluids within a unified port-Hamiltonian (pH) model…
View article: Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems Open
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 mesh-free data-based approximation method for the value fu…
View article: Dictionary-based Online-adaptive Structure-preserving Model Order Reduction for Parametric Hamiltonian Systems
Dictionary-based Online-adaptive Structure-preserving Model Order Reduction for Parametric Hamiltonian Systems Open
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally, Hamil…
View article: Improved a posteriori Error Bounds for Reduced port-Hamiltonian Systems
Improved a posteriori Error Bounds for Reduced port-Hamiltonian Systems Open
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 can be bounded by residual-based methods, which are typicall…
View article: A novel model extended from the Bouguer-Lambert-Beer law can describe the non-linear absorbance of potassium dichromate solutions and microalgae suspensions
A novel model extended from the Bouguer-Lambert-Beer law can describe the non-linear absorbance of potassium dichromate solutions and microalgae suspensions Open
Introduction: The Bouguer-Lambert-Beer law is widely used as the fundamental equation for quantification in absorption spectroscopy. However, deviations from the Bouguer-Lambert-Beer law have also been observed, such as chemical deviation …
View article: Randomized Symplectic Model Order Reduction for Hamiltonian Systems
Randomized Symplectic Model Order Reduction for Hamiltonian Systems Open
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). Recently, symplectic methods like the complex singular va…
View article: Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling
Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling Open
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-output maps that are governed by parametrized partial diffe…