| Private Homepage | https://www.uni-muenster.de/amm/ohlberger |
| Research Interests | Numerical analysis for partial differential equations Model reduction for parametrized partial differential equations Machine Learning and Scientific Computing Development and analysis of numerical multiscale methods Software development |
| Selected Publications | • Klein, Benedikt; Ohlberger, Mario; Schuster, Thomas Adaptive Reduced-Basis Trust-Region Methods for Defect Identification in Elastic Materials. , 2026 online • Kotowski, Dawid; Ohlberger, Mario A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications. , 2026 online • Klein, Benedikt; Ohlberger, Mario Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization. Advances in Computational Mathematics Vol. 52 (19), 2026 online • Kartmann, Michael; Klein, Benedikt; Ohlberger, Mario; Schuster, Thomas; Volkwein, Stefan Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems. Inverse Problems Vol. 41 (12), 2025 online • Gander, Martin J; Ohlberger, Mario; Rave, Stephan A Parareal Algorithm with Spectral Coarse Solver. , 2025 online • Engwer, Christian; Ohlberger, Mario; Renelt, Lukas Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems. , 2025 online • Keil Tim, Ohlberger Mario A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 58, 2024 online • Kartmann, Michael; Keil, Tim; Ohlberger, Mario; Volkwein, Stephan; Kaltenbacher, Barbara Adaptive Reduced Basis Trust Region Methods for Parameter Identification Problems. Computational Science and Engineering Vol. 1 (3), 2024 online • Haasdonk B, Kleikamp H, Ohlberger M, Schindler F, Wenzel T A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs. SIAM Journal on Scientific Computing Vol. 45 (3), 2023 online • Keil T, Kleikamp H, Lorentzen R, Oguntola M, Ohlberger M Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery. Advances in Computational Mathematics Vol. 2022 (48), 2022 online |
| Selected Projects | • Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure The Cluster "Mathematics Münster: Dynamics – Geometry – Structure" advances cutting-edge research by implementing integrated approaches to solve fundamental problems across various mathematical disciplines. These approaches combine different techniques, perspectives, or fields of expertise to address challenges comprehensively. online • Mathematical Research Data Initiative - TA2: Scientific Computing Driven by the needs and requirements of mathematical research as well as scientific disciplines using mathematics, the NFDI-consortium MaRDI (Mathematical Research Data Initiative) will develop and establish standards and services for mathematical research data. Mathematical research data ranges from databases of special functions and mathematical objects, aspects of scientific computing such as models and algorithms to statistical analysis of data with uncertainties. It is also widely used in other scientific disciplines due to the cross-disciplinary nature of mathematical methods. online • EXC 2044 - T05: Curvature, shape and global analysis Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global topological and analytical properties, which in general are strongly intertwined. For instance, it is well known that certain positivity assumptions on the curvature tensor (a local geometric object) imply topological obstructions of the underlying manifold. online • EXC 2044 - T09: Multiscale processes and effective behaviour Many processes in physics, engineering and life sciences involve multiple spatial and temporal scales, where the underlying geometry and dynamics on the smaller scales typically influence the emerging structures on the coarser ones. A unifying theme running through this research topic is to identify the relevant spatial and temporal scales governing the processes under examination. This is achieved, e.g., by establishing sharp scaling laws, by rigorously deriving effective scale-free theories and by developing novel approximation algorithms which balance various parameters arising in multiscale methods. online • EXC 2044 - T10: Deep learning and surrogate methods In this topic we will advance the fundamental mathematical understanding of artificial neural networks, e.g., through the design and rigorous analysis of stochastic gradient descent methods for their training. Combining data-driven machine learning approaches with model order reduction methods, we will develop fully certified multi-fidelity modelling frameworks for parameterised PDEs, design and study higher-order deep learning-based approximation schemes for parametric SPDEs and construct cost-optimal multi-fidelity surrogate methods for PDE-constrained optimisation and inverse problems. online |
| Topics in Mathematics Münster | T5: Curvature, shape, and global analysis T9: Multi-scale processes and effective behaviour T10: Deep learning and surrogate methods |
| Current Publications | • Gander, Martin J; Ohlberger, Mario; Rave, Stephan A Parareal algorithm without Coarse Propagator?. Domain Decomposition Methods in Science and Engineering XXVIIILecture Notes in Computational Science and Engineering, 2026 online • Klein, Benedikt; Ohlberger, Mario Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization. Advances in Computational Mathematics Vol. 52 (19), 2026 online • Kotowski, Dawid; Ohlberger, Mario A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications. , 2026 online • Klein, Benedikt; Ohlberger, Mario; Schuster, Thomas Adaptive Reduced-Basis Trust-Region Methods for Defect Identification in Elastic Materials. , 2026 online • Kabanov, Dmitry I.; Rave, Stephan; Ohlberger, Mario MaRDI Open Interfaces for Interoperable Nonlinear Optimization. , 2026 online • Kabanov, Dmitry I.; Rave, Stephan; Ohlberger, Mario Software package MaRDI Open Interfaces for improved interoperability in numerical optimization. , 2026 online • Gander, Martin J; Ohlberger, Mario; Rave, Stephan A Parareal algorithm without Coarse Propagator?. Domain Decomposition Methods in Science and Engineering XXVIIILecture Notes in Computational Science and Engineering, 2026 online • Klein, Benedikt; Ohlberger, Mario Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization. Advances in Computational Mathematics Vol. 52 (19), 2026 online • Kotowski, Dawid; Ohlberger, Mario A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications. , 2026 online |
| Current Projects | • Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure The Cluster "Mathematics Münster: Dynamics – Geometry – Structure" advances cutting-edge research by implementing integrated approaches to solve fundamental problems across various mathematical disciplines. These approaches combine different techniques, perspectives, or fields of expertise to address challenges comprehensively. online • EXC 2044 - T05: Curvature, shape and global analysis Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global topological and analytical properties, which in general are strongly intertwined. For instance, it is well known that certain positivity assumptions on the curvature tensor (a local geometric object) imply topological obstructions of the underlying manifold. online • EXC 2044 - T09: Multiscale processes and effective behaviour Many processes in physics, engineering and life sciences involve multiple spatial and temporal scales, where the underlying geometry and dynamics on the smaller scales typically influence the emerging structures on the coarser ones. A unifying theme running through this research topic is to identify the relevant spatial and temporal scales governing the processes under examination. This is achieved, e.g., by establishing sharp scaling laws, by rigorously deriving effective scale-free theories and by developing novel approximation algorithms which balance various parameters arising in multiscale methods. online • EXC 2044 - T10: Deep learning and surrogate methods In this topic we will advance the fundamental mathematical understanding of artificial neural networks, e.g., through the design and rigorous analysis of stochastic gradient descent methods for their training. Combining data-driven machine learning approaches with model order reduction methods, we will develop fully certified multi-fidelity modelling frameworks for parameterised PDEs, design and study higher-order deep learning-based approximation schemes for parametric SPDEs and construct cost-optimal multi-fidelity surrogate methods for PDE-constrained optimisation and inverse problems. online • Mathematical Research Data Initiative - TA2: Scientific Computing Driven by the needs and requirements of mathematical research as well as scientific disciplines using mathematics, the NFDI-consortium MaRDI (Mathematical Research Data Initiative) will develop and establish standards and services for mathematical research data. Mathematical research data ranges from databases of special functions and mathematical objects, aspects of scientific computing such as models and algorithms to statistical analysis of data with uncertainties. It is also widely used in other scientific disciplines due to the cross-disciplinary nature of mathematical methods. online | mario dot ohlberger at uni-muenster dot de |
| Phone | +49 251 83-33775 |
| FAX | +49 251 83-32729 |
| Room | 120.010 |
| Secretary | Sekretariat Wernke Frau Silvia Wernke Telefon +49 251 83-35052 Fax +49 251 83-32729 Zimmer 120.001 |
| Address | Prof. Dr. Mario Ohlberger Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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