Forschungsseminar Dynamical Systems and Neuronal Networks

Im Forschungsseminar zur Angewandten Mathematik werden regelmäßig aktuelle fachmathematische Forschungsprojekte vorgestellt und diskutiert. Das Forschungsseminar Angewandte Mathematik findet im Mathematik-Labor "Mathe ist mehr" I 1.07 oder im Mathematischen Umweltlabor I 0.07. statt.

Im Wintersemester 2024/25 gibt es ab 22.10.24 eine Vortragsreihe zum Thema

Dynamical Systems and Neuronal Networks

von Dr. Sandesh Athni Hiremath, RPTU Kaiserslautern Landau, FB Maschinenbau und Elektrotechnik

Course contents:
In this course students shall learn the fundamental principles governing complex systems via the theory of
dynamical systems. We shall mainly rely on PDEs and ODEs as prototypical models to capture the dynamics
of various systems from vehicle motion to the spreading of diseases.

In the first quarter of the course, we shall make a brief recapitulation of the basic topics such as wellposedness, phase space diagrams, stability theory and bifurcation theory, classes of PDEs and also look at standard numerical methods for solving
ODEs and PDEs.

With the emergence of neural networks as universal function approximators they offer
compelling advantages for dealing with complex and high-dimensional PDEs and ODEs. The course shall
focus on understanding how neural networks and the concepts of machine learning can be used to obtain
solutions to different types of dynamical systems especially the ones specified using PDEs and ODEs.

Going further, we shall also focus on the problem of estimating unobserved states and the problem of controlling
the system states based on partial observations with the help of neural networks. Finally, we shall see
how the three core blocks of prediction, estimation and control can be integrated seamlessly in a network
to obtain a generic unified algorithm for solving dynamical problems.

By the course's end, students will have gained a solid foundational understanding of dynamical systems, ODEs, PDEs and neural networks, equipped with analytical and computational tools to address interdisciplinary problems effectively.

Kurs URL: https://klips.rptu.de/v/159977