The seminar will take place Wednesdays 09:15-10:45 in
G29-E037. The first introductory session starts on October
28. Here we discuss possible topics and start the process of
allocating these projects and topics to you. Starting mid December
we plan to have first presentations of projects and talks.
Due to Covid-19 we will have to be flexible and will
organize the seminar in a hybrid fashion. All online parts as well as broadcasts of sessions at the University will happen in the seminar's Zoom channel.
This seminar is a joint event of the faculties for computer
science and mathematics. Students will give talks or present
projects on different mathematical and numerical aspects of
deep neural networks used for physical simulations. The focus
can either be on the presenation of the underlying mathematical
theory or on the implementation of approaches and a
demonstration and ciritical discussion of the results.
Mittwoch, 13.01. Jonathan Irmscher.
A. R. Barron.
Approximation and Estimation Bounds for Artificial Neural Networks. Machine Learning, 14(1):115-133, jan 1994.
Mittwoch, 20.01. Henry von Wahl H. Bölcskei, P. Grohs, G. Kutyniok, and
P. Petersen.
Optimal Approximation with Sparsely Connected Deep Neural Networks. SIAM Journal on Mathematics of Data Science, 1(1):8-45, jan 2019.
Mittwoch, 27.01. Robert Piel, Robert Brockhoff E. Haber, L. Ruthotto
Stable architectures for deep neural networks. Inverse Problems 34(1):014004, 2017.
Mittwoch, 03.02. + Extratermin
Leopold Latsch, Martyna Minakowska, Martyna Soszynska W. E, B. Yu.
The deep ritz method: A deep learning-based numerical
algorithm for solving variational problems. Communications
in Mathematics and Statistics, 6(1):1-12, 2018. L. Lu, X. Meng, Z. Mao, G.E. Karniadakis
DeepXDE: A deep learning library for solving differential equations.
https://arxiv.org/abs/1907.04502
Piotr Minakowski
Approximation of Elasticity Problems with Deep Neural Networks
Mittwoch, 10.02. Harshit Kapadia
Further Topics:
C. Gin, B. Lusch, S. L. Brunton, and
J. N. Kutz.
Deep Learning Models for Global Coordinate Transformations that Linearize PDEs. arXiv e-prints, page arXiv:1911.02710, Nov. 2019.
P. Grohs, F. Hornung, A. Jentzen, and
P. Zimmermann.
Space-time error estimates for deep neural network approximations for differential equations. arXiv e-prints, page arXiv:1908.03833, Aug. 2019.
G. Kutyniok, P. Petersen, M. Raslan, and
R. Schneider.
A Theoretical Analysis of Deep Neural Networks and
Parametric PDEs. mar 2019.
W. E, B. Yu.
The deep ritz method: A deep learning-based numerical
algorithm for solving variational problems. Communications
in Mathematics and Statistics, 6(1):1-12, 2018.
E. Haber, L. Ruthotto.
Stable architectures for deep neural networks. Inverse Problems, 34(1):014004, dec 2017.
Audience
This seminar is intended for students in Master programs of
mathematics and computer science.