Mathematical models play an indispensable, yet often hidden role in our daily life and our understanding of nature. A typical example is the weather forecast, in which complex systems of differential equations, that describe the basic laws of thermo- and hydrodynamics, are simulated. Other models can be found in epidemiology (describing the spreading of infectious diseases), finance and economics (e.g., models for minimization of costs or maximization of profits under constraints, or the determination of fair option prices), or engineering (e.g., artificial neural networks, search engines).
In this presentation, I will derive a few simple mathematical models and discuss their usefulness, but also limitations. I will demonstrate how such models can be simulated to obtain approximate solutions for forecasting certain dynamics in the future. Moreover, instead of only simulating a future behavior, one may want to control and optimize the model to obtain a desired solution behavior. I will show a few such applications of control in engineering applications.
In order to make all the above-mentioned applications computationally feasible, model reduction is often a necessary step to find an approximate model describing the dynamics with a significantly lower number of variables. In the last part of the presentation, I will present some ongoing research in the field of model reduction in which an underlying reproducing kernel Hilbert space structure is exploited.
Matthias Voigt studied mathematics at Chemnitz University of Technology from 2004 to 2010. Thereafter, he was a doctoral student at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg and obtained his doctoral degree from the Faculty of Mathematics of the Otto von Guericke University of Magdeburg in 2015. During his doctoral studies he has also done a research visit at the Courant Institute of Mathematical Sciences in New York. Between 2014 and 2021 he was research associate at Technische Universität Berlin before he took over a W3 substitute professorship at Universität Hamburg from 2019 to 2021.
From 2021-2026, Matthias Voigt was assistant professor with tenure track at UniDistance Suisse, before he was promoted to associate professor in 2026. He is currently acting as the Vice-Dean of the Faculty of Mathematics and Computer Science and the study program director of the B.Sc. program in Mathematics and the M.Sc. program in Artificial Intelligence.
His main research interests are in systems and control (differential-algebraic equations, optimal and robust control, port-Hamiltonian systems), numerical linear algebra (in particular, structured and nonlinear eigenvalue problems, matrix equations), and model reduction and system identification.
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