131 citations · 545 across the 59 of their papers we have counts for
61 papers
Software package MaRDI Open Interfaces for improved interoperability in numerical optimization
Dmitry I. Kabanov, Stephan Rave, Mario Ohlberger
To address the challenges of interoperability in computational science, we present the latest updates to the software package MaRDI Open Interfaces. This software package aims to d…
MaRDI Open Interfaces for Interoperable Nonlinear Optimization
Dmitry I. Kabanov, Stephan Rave, Mario Ohlberger
MaRDI Open Interfaces is a software package that aims to improve interoperability in scientific computing, particularly, for nonlinear optimization. To this end, this package holds…
Adaptive Reduced-Basis Trust-Region Methods for Defect Identification in Elastic Materials
Benedikt Klein, Mario Ohlberger, Thomas Schuster
Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displace…
A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications
Dawid Kotowski, Mario Ohlberger
This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with differe…
A Parareal Algorithm with Low-Rank Coarse Solvers
Martin J. Gander, Mario Ohlberger, Stephan Rave
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from truncated SVD approximations of the transfe…
Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems
Christian Engwer, Mario Ohlberger, Lukas Renelt
We investigate parametrized variational problems where for each parameter the solution may originate from a different parameter-dependent function space. Our main motivation is the…
Improving Interoperability in Scientific Computing via MaRDI Open Interfaces
Dmitry I. Kabanov, Stephan Rave, Mario Ohlberger
MaRDI Open Interfaces is a software project aimed at improving reuse and interoperability in Scientific Computing by alleviating the difficulties of crossing boundaries between dif…
Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization
Benedikt Klein, Mario Ohlberger
This article builds on the recently proposed RB-ML-ROM approach for parameterized parabolic PDEs and proposes a novel hierarchical Trust Region algorithm for solving parabolic PDE…
Adaptive Model Hierarchies for Multi-Query Scenarios
Hendrik Kleikamp, Mario Ohlberger
In this contribution we present an abstract framework for adaptive model hierarchies together with several instances of hierarchies for specific applications. The hierarchy is part…
A Parareal algorithm without Coarse Propagator?
Martin J. Gander, Mario Ohlberger, Stephan Rave
The Parareal algorithm was invented in 2001 in order to parallelize the solution of evolution problems in the time direction. It is based on parallel fine time propagators called F…
Construction of local reduced spaces for Friedrichs' systems via randomized training
Christian Engwer, Mario Ohlberger, Lukas Renelt
This contribution extends the localized training approach, traditionally employed for multiscale problems and parameterized partial differential equations (PDEs) featuring locally…
Local training and enrichment based on a residual localization strategy
Tim Keil, Mario Ohlberger, Felix Schindler +1
To efficiently tackle parametrized multi and/or large scale problems, we propose an adaptive localized model order reduction framework combining both local offline training and loc…
Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems
Christian Engwer, Mario Ohlberger, Lukas Renelt
This contribution introduces a model order reduction approach for an advection-reaction problem with a parametrized reaction function. The underlying discretization uses an ultrawe…
An optimally stable approximation of reactive transport using discrete test and infinite trial spaces
Lukas Renelt, Christian Engwer, Mario Ohlberger
In this contribution we propose an optimally stable ultraweak Petrov-Galerkin variational formulation and subsequent discretization for stationary reactive transport problems. The…
Adaptive Localized Reduced Basis Methods for Large Scale Parameterized Systems
Tim Keil, Mario Ohlberger, Felix Schindler
In this contribution, we introduce and numerically evaluate a certified and adaptive localized reduced basis method as a local model in a trust-region optimization method for param…
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-…
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…
Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain
Hendrik Kleikamp, Mario Ohlberger, Stephan Rave
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, li…
Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery
Tim Keil, Hendrik Kleikamp, Rolf J Lorentzen +2
In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer floodi…
A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems
Tim Keil, Mario Ohlberger
In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for…
Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD
Tobias Leibner, Maja Matis, Mario Ohlberger +1
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties…
A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-Ion Battery Cells
M. Landstorfer, M. Ohlberger, S. Rave +1
In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general inter…
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…
Model Reduction for Large Scale Systems
Tim Keil, Mario Ohlberger
Projection based model order reduction has become a mature technique for simulation of large classes of parameterized systems. However, several challenges remain for problems where…