Teams
Numerical Linear and Multilinear Algebra (NLMA)
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.
Moreover, we investigate the solution of special linear systems of equations arising in PDE control and model reduction algorithms.
Model Order Reduction (MOR)
In order to get a deep insight into the underlying process, dynamics, structure or devices, modeling and simulation are unavoidable in many research and application fields. The resulting mathematical models are usually in the form of partial differential equations. To simulate such models, spatial (-time) discretization is necessary, which results in large-scale, complex systems with enormous number of equations. The simulation becomes time-consuming because of the large scale and complexity of the systems.
Physics-Enhanced Machine Learning (PML)
With the rapid development in measurement technology and computing power, our interest lies in learning models that explain underlying dynamical behaviors and draw meaningful conclusions from the learned model. The PML team is particularly dedicated to developing innovative machine learning methodologies by incorporating fundamental principles and empirical knowledge of the process. Moreover, we focus on inferring low-dimensional models using machine learning tools, thus accelerating online simulations of high-fidelity models.
Computer Aided Control System Design (CACSD)
Computer aided control system design refers to numerical methods for the design of controllers and on modeling, discretization, and simulation of systems with controls and observations. The work on effective control setups combines methods from the fields of model order reduction, matrix equations, and scientific computing.
Simulation of Energy Systems (SES)
Modeling and simulation of fluids in large networks is a challenging problem, especially if the simulation is used to provide solutions to optimal control problems or other optimization questions. Our first goal is to be able to simulate this systems in a stable and efficient manner as truely transient systems, considering in particular the underlying network stucture.
Structured Dynamical Systems (SDS)
Accurate modeling of dynamical systems is crucial for engineering studies. Typically, dynamical processes have intrinsic structures, including time-delays, second-order and factional derivatives. These processes may be subjected to 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.
Data, Infrastructure, Software & Computing (DISC)
In times of energy transition and reproducibility crisis, the team is concerned both with the research of new algorithms for power-aware computing and with the documentation and archiving of computer-based experiments. In addition to the software, infrastructural measures for data storage according to the FAIR principles as well as the reproducible execution of experiments are investigated. An additional pillar is formed by the methods of scientific high-performance computing.