The research interests of the Mathematics in Simulation and Education group include diverse aspects in the area of mathematical modelling in system simulation. These include, but are not limited to, the following areas:

•     Physiological modelling
•     Simulation of behavioural models
•     Control mathematics and dynamical systems
•     Integration of machine learning methods in system simulation

Physiological modelling ranges from models of simple functional organs, such as the kidney, to more complex controlled components, such as the thyroid gland. The focus is always on verification and validation with data in order to do justice to application-oriented research in cooperation with experts. Models in this area also go further, such as entropy-based models, which are used in the context of sleep and anesthesia research based on EEG data.

Behavioural models are also used in a physiological context, but are not limited to this. These models are data-driven "black box" (or "grey box") modelling and can be applied to many data modelling problems.

Control mathematics offers a wide field of applications in the area of modelling and simulation, starting with modelling based on physical laws and assumptions (physical modelling, first principal modelling), this area also holds the challenge of various optimisation problems of simulation tasks through control. The associated dynamic systems enable simulation studies on parameter sensitivity up to statistical investigations of control loops.

Machine learning is a topic that also influences the field of simulation. In particular, such methods are used in questions of control or regulation of simulations or questions that allow optimisation with the help of simulations. This is directly related to the topic of sleep and anaesthesia research, but optimisation with the help of reinforcement learning approaches is also of interest.

In addition, research and development is also included in the working group in the area of education and related forms of teaching and learning. This includes, among other things, the tasks of developing CAS algorithms for the automatic creation and assessment of mathematical tasks. In connection with this, didactic questions must also be critically questioned and answered in a reflective manner.