A Framework Including Artificial Neural Networks in Modelling Hyb Dynamical Systems
34th Edition
Published on 1. January 2021
Book
Paperback/Softback
978-3-903311-12-1 (ISBN)
Description
About the Book
Modelling dynamical systems by equations and modelling dynamical behaviour by neural nets are up to now different worlds. This PhD thesis tries to combine these two worlds in the area of hybrid dynamical systems. The author first introduces modelling standards for hybrid dynamical systems using hybrid state automata followed by neural network practices for dynamic behaviour. Based on these two areas the author develops a framework, which allows to replace certain elements of hybrid models by neural networks, as sketched by the cover pictures.
On a mathematical
basis of extending hybrid state automata by neural nets and training methods, the thesis discusses three different possibilities for application: the approximation of local dynamic behaviour, the prediction of the discrete processes and the replacement of the entire hybrid system applying neural networks. The defined formalism standardises the use of feed-forward networks in hybrid modelling and in general to enable an analysis of different network structures.
Modelling dynamical systems by equations and modelling dynamical behaviour by neural nets are up to now different worlds. This PhD thesis tries to combine these two worlds in the area of hybrid dynamical systems. The author first introduces modelling standards for hybrid dynamical systems using hybrid state automata followed by neural network practices for dynamic behaviour. Based on these two areas the author develops a framework, which allows to replace certain elements of hybrid models by neural networks, as sketched by the cover pictures.
On a mathematical
basis of extending hybrid state automata by neural nets and training methods, the thesis discusses three different possibilities for application: the approximation of local dynamic behaviour, the prediction of the discrete processes and the replacement of the entire hybrid system applying neural networks. The defined formalism standardises the use of feed-forward networks in hybrid modelling and in general to enable an analysis of different network structures.
More details
Person
Author
Stefanie Nadine Winkler studied Technical Mathematics at the Vienna University of Technology (TU Wien). Already in her bachelor curriculum she got involved n modelling and simulation. At master level, she put emphasis on two subjects - modelling methods and system simulation, as well as Blended Learning for modelling and simulation and basic mathematics.
The first topic led her to a benchmarking master thesis on Comparative Mathematical Modelling of Groundwater Pollution, where she showed her interest and her abilities in analysing different modelling approaches. The work in E-Learning opened her a door into the TU Wien AKMATH Group, where she organised and executed the introductory mathematic courses for all beginners at TU Wien including managing the E-Learning content team developing interactive online examples for mathematics. After the master thesis, she continued her work as part of the
E-Learning group as well as her scientific work in the PhD curriculum. She investigated various approaches for modelling hybrid systems and analysed neural network approaches, which she combined in her PhD on neural net modelling for hybrid systems. Her deep knowledge in the Maplebased Math E-Learning system (Maple-TA/Möbius) resulted in consultancy work at European universities representing Maplesoft Europe and DigitalEd. After her PhD, she left university and started working for the management consulting firm d-fine Austria.