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S. Winkler:
"A Framework Including Artificial Neural Networks in Modelling Hybrid Dynamical Systems";
Supervisor, Reviewer: F. Breitenecker, G. Music, A. Körner; Institut für Analysis und Scientific Computing, 2020; oral examination: 2020-02-18.

This work is situated in the research field mathematical modelling and simulation and focuses on the field of hybrid modelling. This wording has different meanings but superficially speaking it always stands for a combination of different modelling methods. In terms of mathematical modelling hybrid defines a combination of multiple modelling approaches in one model description.

Especially hybrid dynamical models, which not only consist of different discrete submodels but also continuous structures to represent real-world systems, are the focus of this thesis. Switching from one submodel to another state variables or even underlying mathematical description change at a certain time, called discrete events. In order to describe such hybrid systems, different formalisms were introduced over the last years and decades. The usage of an automaton, more simulation driven formalism DEVS&DESS as well as a very common approach, piecewise linear affine systems, will be investigated.

The goal of this thesis is to compare these approaches regarding their advantages and disadvantages related to practicability and accuracy as well as establishing new methods for modelling and simulation in hybrid dynamical systems. Due to the fact that the availability of data and the possibilities to gather such information are increasing data modelling should be considered as a possible approach for hybrid modelling.