Modeling-Simulation-Optimization of discrete, continuous, and stochastic systems
Mathematical models of systems, e.g. in modern Information Technology, quite often exhibit both discrete and continuous aspects as well as their interaction. This concerns the modeling of time in dynamical systems either as a continuum or a finite/countable number of instances when observations are taken or when control acts, and strongly influences the analysis of the qualitative behavior of such systems as well as their design via continuous or combinatorial optimization methods, respectively. Moreover, robustness with respect to uncertainty caused by noise or perturbations is a crucial issue in such systems and needs skillful stochastic modeling as well as estimation, prediction and model validation. The rigorous and efficient treatment of these problems requires knowledge from a wide range of mathematical fields, namely Dynamical Systems, Statistical Data Analysis, Nonlinear and Combinatorial Optimization, Discrete Mathematics and Inverse Problems.
The DK MSO is supported by the Karl Popper Kolleg of the AAU.
Numerical and qualitative analysis of dynamical systems, Nonlinear and combinatorial optimization, Extremal discrete structures, Bayesian spatio-temporal prediction and design, Inverse problems
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