Teams

Numerical Linear and Multilinear Algebra

Lead: Prof. Dr. Peter Benner
We study numerical methods for linear and nonlinear eigenvalue problems. This includes the development and analysis of new algorithms, (backward) error analysis, and the derivation of the associated (relative) perturbation theory. Special attention is given to linear, generalized, and polynomial eigenproblems with spectral symmetries. Moreover, we investigate the solution of special linear systems of equations arising in PDE control and model reduction algorithms.
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Model Order Reduction

Lead: Dr. Lihong Feng
Our research aims at reducing the computational complexity of large-scale complex dynamical systems arising from various fields. Small reduced-order models are computed to serve as surrogates for the large systems in simulation, optimization, control, and uncertainty quantifi-cation, in order to greatly reduce the computational burden of these tasks, while still retaining fidelity.
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Physics-Enhanced Machine Learning

Lead: Dr. Igor Pontes Duff Peirera
The PML team is dedicated to developing innovative machine learning algorithms for learning dynamical systems incorporating empirical knowledge. Moreover, for high-dimensional data, we focus on identifying low-dimensional embeddings using deep learning to ease the engineering design process for complex systems.
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Computer Aided Control System Design

Lead: Prof. Dr. Alexander Zuyev
The CACSD team works on numerical methods for the design of controllers as well as tools for modeling, discretization, and simulation of systems with controls and observations. The work on effective control setups combines methods from the fields of MOR, matrix equations, and scientific computing.
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Simulation of Energy Systems

Lead: Dr. Sara Grundel
Modeling and simulation of energy systems are key tools to realizing a carbon neutral world. We focus on the efficient and accurate simulation of the gas and power grid. In order to achieve this goal, we use our expertise as well as that of the greater mathematical community in surrogate modeling. [more]

Structured Dynamical Systems

Lead: Dr. Igor Pontes Duff Pereira
Dynamical processes have intrinsic dynamical structures, including time-delays, second-order derivatives, and stochastic and switching behaviors. The SDS team dedicates its efforts to develop new theoretical and computational results to allow efficient simulation, optimization, and control for high-fidelity structured models. [more]

Data, Infrastructure, Software & Computing

Lead: Dr. Jens Saak
Concerned with the research of algorithms for power-aware computing and the documentation & archiving of computer-based experiments, we investigate measures for data storage according to the FAIR principles, the reproducible execution of experiments and methods of scientific high-performance computing. [more]