University of Bayreuth, Press Release Nr. 105/2021 28 July 2021

# Bayreuth mathematics investigating the foundations of artificial intelligence

Mathematics in Bayreuth is deeply involved in two research projects in the German Research Foundation (DFG) Priority Programme 2298 "Theoretical Foundation of Deep Learning". The main goal of this priority programme is to develop a comprehensive theoretical foundation for Deep Learning. DFG is providing the University of Bayreuth with € 418,800 for the two projects over the next three years.

Currently, Deep Learning - a sub-field of Artificial Intelligence - is experiencing unprecedented success in real-world applications: in autonomous driving, in power grid control, and in the health sector, for instance. At the same time, Deep Learning-based methods are making a strong impact on science, often replacing state-of-the-art classical model-based methods to solve mathematical problems.

But deep neural network research largely lacks the mathematical foundations needed to minimise the error-proneness of this technology. The projects led by Prof. Dr. Lars Grüne and Prof. Dr. Anton Schiela, Joint Chairs of Applied Mathematics at the University of Bayreuth, deal with various aspects of this type of machine learning.

Prof. Grüne's project revolves around the question of precisely where deep neural networks are suitable for high-dimensional control and regulation tasks, i.e. for tasks that depend on very many influencing variables, and where not. Such applications exist, among other things, in the control of large networks, such as the management of power grids with a high number of renewable energy sources. It is well-known in practice that learning methods in artificial intelligence using deep neural networks work very well for some such tasks, but not at all for others. The project is looking for the mathematical structures of such control tasks that underlie this phenomenon. Research into these mathematical principles should make it possible to better assess the chances of success of such learning procedures, and to design control tasks in such a way as to make them more efficient to perform. This can, for example, make power supply in a system of numerous, decentralised power sources - as brought about by the switch to renewable energy - more reliable.

Prof. Schiela's project, which is being conducted in cooperation with Prof. Dr. Roland Herzog from the University of Heidelberg, is researching new methods in mathematical optimisation for training deep neural networks. On the one hand, these should enable more efficient training and, on the other, automate the determination of parameters, which usually still have to be set by hand very laboriously. This should make the artificial intelligence training process simpler and more reliable. Moreover, this project does not aim at any particular application of deep neural networks, but will develop methods that can be used in very many different situations.

The priority programme, which involves a good 20 research projects nationwide, will begin in autumn 2021. Link: https://www.spp2298.de

### Background

Machine learning is a sub-field of artificial intelligence that enables systems to learn from data and improve - by using methods of mathematical optimisation. They are used, among other things, in image processing, for example in the recognition of traffic signs by autonomous systems in cars, and in the control of robots. These traffic signs or robot movements are not programmed in, but are taken from predefined data through so-called training - or "learned". Deep learning is a sub-area of machine learning. It uses neural networks, which are modelled on the structures of the human brain, and large amounts of data (big data).

### Contact

### Prof. Dr. Anton SchielaChair of Applied Mathematics

Phone: +49 (0)921 / 55-3281

E-Mail: anton.schiela@uni-bayreuth.de

Building NW II, Room 3.2 01 533

Universtitätsstraße 30, 95447 Bayreuth

### Prof. Dr. Lars GrüneChair of Applied Mathematics

Phone: +49 (0)921 / 55-3270

E-Mail: lars.gruene@uni-bayreuth.de

Office: Building NW II, Room 3.2 01 532

Universtitätsstraße 30, 95447 Bayreuth

### Anja-Maria MeisterPR Spokesperson University of Bayreuth

Phone: +49 (0) 921 / 55-5300

E-mail: anja.meister@uni-bayreuth.de

Universitätsstraße 30

D-95447 Bayreuth