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Hochdimensionale Partielle Differentialgleichungen SoSe 2019

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Hochdimensionale Partielle Differentialgleichungen

Termine
Mi
12.00 - 14:00
Seminar
MA564
Prof. Dr. Reinhold Schneider


Koordination Vorträge
MA567
Leon Sallandt
Sekretariat 
MA568

Die Vorbesprechung zum Seminar findet am Mittwoch, den 10. April 2019 um 12:00 Uhr im Raum MA564 statt

Beschreibung

Das Seminar richtet sich an Studierende der Studiengänge Mathematik, Informatik und Physik. 

Es werden unter anderem Vorträge zu den folgenden Themenbereichen gehalten:

  • Partielle Differentialgleichungen
  • Tensorproduktapproximation
  • Numerische Lösungsverfahren
  • Machine Learning

Studierende sind herzlich willkommen eigene Vorträge zu halten.

Literatur

Als Literatur sind die folgenden Bücher geeignet:

  • Roger A. Horn, Charles R. Johnson: "Matrix Analysis, Second Edition", Cambridge University Press
  • Wolfgang Hackbusch: "Tensor Spaces and Numerical Tensor Calculus", Springer Series in Computational Mathematics, Vol. 42, Springer
  • P.-A. Absil, R. Mahony, R. Sepulchre: "Optimization Algorithms on Matrix Manifolds", Princeton University Press

Information

Introduction to Machine Learning Deep neural networks 1 (Goodfellow "Deep Learning") Deep neural networks 2 (Goodfellow "Deep Learning")

Approximation theory neural networks (Mhaskar, Master's Thesis (send me an e-mail))

Langevin dynamics (Pavliotis "Stochastic Processes and Applications")

Discontinuous Galerkin (Ern "Mathematical Aspects of Discontinuous Galerkin Methods")

Spectral methods (Quarteroni and Valli "Numerical Approximation of Partial Differential Equations")

Semi-Lagrangian methods for Hamilton-Jacobi-Bellman equation (Tonon and Aronna and Kalise "Optimal Control: Novel Directions and Applications")

Reinforcement learning / Hamilton-Jacobi-Bellman equation (Bertsekas "Dynamic Programming & Optimal Control")

Viscosity solutions (Bressan "Viscosity Solutions of Hamilton-Jacobi Equations and Optimal Control Problems" (lecture notes), additionally: Crandall/Lions "Viscosity Solutions of Hamilton-Jacobi Equations"(hard to read))

Introduction to Uncertainty Quantification (lecture notes/sent via e-mail)

 

The Seminar itself will take place on 10./11.7. from 10AM to 3PM (s.t.!) in MA564

Please prepare the presentation in English.

Important information

Dear all,

please confirm that you will hold your presentation, either by coming to my office, or by writing a short e-mail. Please also include in this e-mail whether you need a grade in the end of the seminar. Those who need a grade will have to hold their presentations on thursday. If you do not confirm your participation beforehand, we are unable to plan the schedule for the presentations and thus your presentation might not be included in the plan.

Note that as we do have a lot of presentations, we have decided that it is okay if your group presentation is only 60 min.

Best regards

Leon

Submitting deadline

Dear all,

the deadline for submitting your written summary is the 27th of July 2019, 23:59h. Please send it to me via e-mail as a pdf file. The summary should contain at least 5, but no more than 10 pages.

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