EXC 2044 - T10: Deep learning and surrogate methods
Basic data for this project
Type of project: Subproject in DFG-joint project hosted at University of Münster
Duration at the University of Münster: 01/01/2026 - 31/12/2032 | 1st Funding period
Description
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.
Keywords: Mathematics; Differential geometry; Stochastic analysis, Theory of stochastic processes, Optimisation and calculus of variations, Numerical analysis, machine learning and scientific computing
Website of the project: https://www.uni-muenster.de/MathematicsMuenster/research/programme/topic_deepl-surrogate-methods.shtml
Funding identifier: EXC 2044/2, T10
Funder / funding scheme:
- DFG - Cluster of Excellence (EXC)
Project management at the University of Münster
| Böhm, Christoph | Professur für Theoretische Mathematik (Prof. Böhm) |
| Dereich, Steffen | Professorship for Theory of Probability (Prof. Dereich) |
| Engwer, Christian | Professorship for Applications of Partial Differential Equations |
| Jentzen, Arnulf | Professorship for applied mathematics (Prof. Jentzen) |
| Kuckuck, Benno | Professorship for applied mathematics (Prof. Jentzen) |
| Ohlberger, Mario | Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) |
| Rave, Stephan | Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) |
| Weber, Hendrik | Professorship of Mathematics (Prof. Weber) |
| Wirth, Benedikt | Professorship of Biomedical Computing/Modelling (Prof. Wirth) |
Applicants from the University of Münster
| Böhm, Christoph | Professur für Theoretische Mathematik (Prof. Böhm) |
| Dereich, Steffen | Professorship for Theory of Probability (Prof. Dereich) |
| Engwer, Christian | Center for Nonlinear Science |
| Jentzen, Arnulf | Professorship for applied mathematics (Prof. Jentzen) |
| Kuckuck, Benno | Professorship for applied mathematics (Prof. Jentzen) |
| Ohlberger, Mario | Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) |
| Rave, Stephan | Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) |
| Weber, Hendrik | Professorship of Mathematics (Prof. Weber) |
| Wirth, Benedikt | Professorship of Biomedical Computing/Modelling (Prof. Wirth) |
