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Forschungsseminar Dynamical Systems and Neuronal Networks - Einzelansicht

Grunddaten
Veranstaltungsart Vorlesung/Seminar Langtext
Veranstaltungsnummer Kurztext
Semester WiSe 2024/25 SWS 2
Erwartete Teilnehmer/-innen 10 Max. Teilnehmer/-innen 30
Rhythmus keine Übernahme Belegung Keine Belegpflicht
LV-Kennung (Lehrevaluation) 159977   Kurz-URL https://klips.rptu.de/v/159977
Hyperlink   Durchführungsart Digital
Termine Gruppe: [unbenannt] iCalendar Export für SOGo
  Tag Zeit Rhythmus Termin Prüfungs-
termin
Raum Gebäude / Karte Campus Lehrperson Sprache Bemerkung fällt aus am Max. Teilnehmer/-innen
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Di. 14:00 bis 16:00 c.t. woch 22.10.2024 bis 04.02.2025  I 0.07 Gebäude I Landau        
Gruppe [unbenannt]:
 
 


Zugeordnete Personen
Zugeordnete Personen
Zuständigkeit
Hundertmark, Anna, Prof. Dr. begleitend
Niehaus, Engelbert, Prof. Dr. begleitend
Schmitz, Stephan, Dr. begleitend
Studiengänge
Abschluss
Studiengang Semester Prüfungsversion Studienphase
M.Ed. Gymnasium M.Ed. Gym Mathematik LD (20103) 3 - 4 20103
Zuordnung zu Einrichtungen
AG Numerische Simulation (Prof. Hundertmark)
Inhalt
Lerninhalte

 

Abstract: Dynamical Systems and Neural Networks

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.

 

Contents

• Recap on the basics of ODEs and PDEs from the viewpoint of functional theory

• Recap on numerical methods for ODEs (deterministic methods: Euler, RK, finite difference, finite elements)

• Neural networks (NNs) and approximation theorems

• NNs as a method for solving differential functional equations

• NNs as a method for solving functional state estimation problem

• NNs as a method for solving functional optimization problem

• Different types of NN design for PDEs and ODEs

• Physics informed neural networks, neural differential equations and diffusion models

• Applications in process automation, automated robot and vehicle control

 

Competencies / intended learning achievements

From the lecture students are able to

• refresh the basic foundational concepts and techniques to specify, analyze and solve ODEs and PDEs

• refresh the basic concepts of probability and statistics

• become familiar with stochastic and statistical methods for solving differential equations.

• utilize neural networks and approximation theorems to solve differential equations effectively.

• utilize neural networks for estimating unobserved states of the dynamical system.

• utilize neural networks for synthesizing actuation signals and to design automatic control algorithms for dynamical system.

 

From the (integrated) tutorials students are able to

• become proficient in using relevant python libraries for solving ODEs/PDEs

• apply monte-carlo method for solving ODEs

• apply physics-informed neural networks and related models to real-world problems involving differential equations 

 

 

 

Kommentar

 

 

Dozent:

 Sandesh Athni Hiremath, Dr. rer. nat (Department: Maschinenbau und Verfahrenstechniik) RPTU in Kasertslautern

https://mv.rptu.de/fgs/mec/staff/sandesh-hiremath

 

OLAT Link: https://olat.vcrp.de/auth/RepositoryEntry/4676878415/CourseNode/104543547816611 

Lecture Zoom link:

https://uni-kl-de.zoom-x.de/j/62010681163?pwd=X9LdRqzSmKkaAOKwEerONfYgZfm43e.1



Meeting ID: 620 1068 1163
Passcode: BRh?$+t2

Literatur

Literature

  • Strauss, W. A., Partial Differential Equations- An Introduction, John Wiley & Sons, Inc., New York, 1992
  •  Evans, L. C., Partial differential equations, American Mathematical Society, 2010.
  •  Birkhoff, G.D., Dynamical Systems, Volume 9. American Mathematical Soc., 1927.
  • Goodfellow, I., Bengio, Y., and Courville, A., Deep Learning, MIT press, 2016.
  •  LeCun, Y., Bengio, Y., and Hinton, G., Deep learning, Nature, 521(7553):436–444, 2015
  •  Bishop, C. M., and Others. Pattern Recognition and Machine Learning, Volume 4. Springer New York, 2006.
Bemerkung

Dies ist eine erweiternde Lehrveranstaltung für Promovierende und interessierte Master-Studenten über die modernen Lösungsansätze für Gleichungen der dynamischen Systeme.

Voraussetzungen

Recommended prior knowledge for course participation (informal):

Multivariable calculus, Vector calculus, Linear algebra, Python programming (basic)

 


Strukturbaum
Die Veranstaltung wurde 3 mal im Vorlesungsverzeichnis WiSe 2024/25 gefunden:
M Ed Mathematik R+  - - - 1
M Ed Mathematik Gym  - - - 2
Sonderveranstaltungen  - - - 3
User auf Server node2: 1553