The availability of very large data sets offers new possibilities and challenges for research within the cluster of Mathematics of Computational Science (MCS).
Data-driven science allows the discovery of hidden parameters or functions in dynamical systems from observed data by solving (ill-posed) inverse problems. Also, topics such as uncertainty quantification and model order reduction are rapidly gaining importance. We aim therefore to combine data-driven science with our strong research in dynamical systems, scientific computing, and mathematical systems theory. This will offer new opportunities to obtain more accurate data-driven models in for instance neuroscience, seismic, and turbulence, but also present significant mathematical challenges, such as understanding the mathematical properties of these new models and techniques and deriving and analyzing accurate and efficient numerical discretizations for these novel approaches.
The MCS research team focuses on the following topics in the area of dynamical systems, numerical analysis and scientific computing, and systems and control, in particular their relation with data science.
- Artificial intelligence for medical imaging (Jelmer Wolterink, Christoph Brune)
- Control of partial differential equations (Felix Schwenninger, Anton Stoorvogel, Hans Zwart)
- Computational methods for direct and inverse problems in wave phenomena (Carlos Pérez Arancibia)
- Computational neuroscience and dynamical systems (Hil Meijer)
- Differential Geometry in Theoretical Physics (Frederic P. Schuller)
- Discovery of equations, model sparsity, and uncertainty, deep machine learning for PDEs (Christoph Brune, Silke Glas, Mengwu Guo, Jelmer Wolterink)
- Functional Analysis (Felix Schwenninger)
- High-order fast integral-equation-based partial differential equation solvers. (Carlos Pérez Arancibia)
- High-fidelity and efficient methods for computational fluid dynamics (Philip Leder)
- Inverse problems, data assimilation, and optimal transport on graphs. (Christoph Brune & Matthias Schlottbom)
- Mathematical Robotics (Frederic P. Schuller and Stefano Stramigioli)
- Multi Scale Modeling (Bernard Geurts)
- Scientific machine learning with uncertainty quantification (Mengwu Guo)
- Structure-preserving model reduction (Silke Glas, Philip Lederer, Tomasz Tyranowski)
- Structure preserving numerical discretizations (Matthias Schlottbom, Hans Zwart, Tomasz Tyranowski)
- Variational and geometric methods in inverse problems and machine learning (Marcello Carioni, Josè Iglesias, Christoph Brune)
- Quantum Systems Theory (Hans Zwart, Frederic P. Schuller, Stefano Stramigioli)
MCS is contributing to NDNS+, one of the four mathematics clusters in the Netherlands. Our work is part of the JM Burgers Center for Fluid Mechanics and the DISC research school on Systems and Control. We are active partners of 4TU.AMI, the Applied Mathematics Institute of the three Universities of Technology and the University of Wageningen, PWN, the Netherlands Mathematics Platform and of AI in Mathematics.
Our teaching program prepares students for working in academia and in industry, strengthened by our unique emphasis on close multidisciplinary collaboration.