| Private Homepage | https://stephanrave.de/ |
| 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 | • Kabanov, Dmitry I.; Rave, Stephan; Ohlberger, Mario Improving Interoperability in Scientific Computing via MaRDI Open Interfaces. Journal of Open Research Software Vol. 13 (1), 2025 online • Gander, Martin J; Ohlberger, Mario; Rave, Stephan A Parareal Algorithm with Spectral Coarse Solver. , 2025 online • Gander, Martin J; Ohlberger, Mario; Rave, Stephan A Parareal algorithm without Coarse Propagator?. , 2024 online • Landstorfer M, Ohlberger M, Rave S, Tacke M A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-Ion Battery Cells. European Journal of Applied Mathematics Vol. 34 (3), 2023 online • Keil Tim, Rave Stephan An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition. SIAM Journal on Scientific Computing Vol. 45 (4), 2023 online • Gander Martin, Rave Stephan Localized Reduced Basis Additive Schwarz Methods. Domain Decomposition Methods in Science and Engineering XXVI, 2022 online • Kleikamp Hendrik, Ohlberger Mario, Rave Stephan Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain. MATHMOD 2022 - Discussion Contribution VolumeARGESIM ReportArXiv Vol. 17, 2022 online • Benner, P.; Burger, M.; Göddeke, D.; Himpe, C.; Hintermüller, M.; Heiland, J.; Koprucki, T.; Ohlberger, M.; Rave, S.; Reidelbach, M.; Saak, J.; Schöbel, A.; Tabelow, K. Die Mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative). GAMM Rundbrief Vol. 1/2022, 2022 online • Fritze, René; Rave, Stephan Specification and Validation of Numerical Algorithms with the Gradual Contracts Pattern. Testing Software and SystemsLecture Notes in Computer Science, 2022 online |
| Current Projects | • 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 • EXC 2044 - C4: Geometry-based modelling, approximation, and reduction In mathematical modelling and its application to the sciences, the notion of geometry enters in multiple related but different flavours: the geometry of the underlying space (in which e.g. data may be given), the geometry of patterns (as observed in experiments or solutions of corresponding mathematical models), or the geometry of domains (on which PDEs and their approximations act). We will develop analytical and numerical tools to understand, utilise and control geometry, also touching upon dynamically changing geometries and structural connections between different mathematical concepts, such as PDE solution manifolds, analysis of pattern formation, and geometry. online | stephan.rave@uni-muenster.de |
| Phone | +49 251 83-35061 |
| FAX | +49 251 83-32729 |
| Room | 120.023 |
| Secretary | Sekretariat Wernke Frau Silvia Wernke Telefon +49 251 83-35052 Fax +49 251 83-32729 Zimmer 120.001 |
| Address | Dr. Stephan Rave Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster |
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