Christoph Schwab: Catalogue data in Autumn Semester 2017

Name Prof. Dr. Christoph Schwab
Seminar für Angewandte Mathematik
ETH Zürich, HG G 57.1
Rämistrasse 101
8092 Zürich
Telephone+41 44 632 35 95
Fax+41 44 632 10 85
RelationshipFull Professor

401-3650-67LNumerical Analysis Seminar: Tensor Numerics and Deep Neural Networks Information Restricted registration - show details
Number of participants limited to 10.
4 credits2SC. Schwab
AbstractThe seminar addresses recently discovered
_mathematical_ connections between Deep Learning
and Tensor-formatted numerical analysis,
with particular attention to
the numerical solution of partial differential equations,
with random input data.
ObjectiveThe aim of the seminar is to review recent [2015-]
research work and results,
together with recently published software
such as the TT-Toolbox, and Google's TENSORFLOW.

The focus is on the mathematical analysis and
interpretation of current learning approaches
and related mathematical and technical fields, e.g.
high-dimensional approximation, tensor structured numerical methods
for the numerical solution of highdimensional PDEs,
with applications in computational UQ.
For theory, we refer to the references in the survey
Numerical experiments will be done with TENSORFLOW and with the
TT toolbox at
Lecture notesThe seminar will study a set of 10 orginial papers from 2015 to today.
LiteratureHelmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Optimal Approximation with Sparsely Connected Deep Neural Networks

N. Cohen, O. Sharir, Y. Levine, R. Tamari, D. Yakira and A. Shashua (May 2017):
Analysis and design of convolutional networks via hierarchical tensor decompositions,

N. Cohen and A. Shashua (March 2016),
Convolutional rectifier networks as generalized tensor decompositions,
Technical report, arXiv:1603.00162.
Proceedings of The 33rd International Conference on Machine Learning, pp. 955-963, 2016.

N. Cohen, O. Sharir and A. Shashua (Sept. 2015),
On the expressive power of deep learning: A tensor analysis,
Technical report, arXiv:1509.05009.
Journal-ref: 29th Annual Conference on Learning Theory, pp. 698-728, 2016.
Prerequisites / NoticeCompleted BSc MATH exam.
401-4645-67LNumerics for Computational Uncertainty Quantification Information 10 credits3V + 2UC. Schwab
AbstractThe course presents the mathematical foundation of various numerical methods
for the efficient quantification of uncertainty in partial differential equations.
Mathematical foundations include high dimensional polynomial approximation,
sparse grid approximations, generalized polynomial chaos expansions and their
summability properties, as well the computer implementation in model problems.
ObjectiveThe course will provide a survey of the mathematical properties and
the computational realization of the most widely used numerical methods
for uncertainy quantification in PDEs from engineering and the sciences.
In particular, Monte-Carlo, Quasi-Monte Carlo and their multilevel extensions
for PDEs, Sparse grid and Smolyak approximations, stochastic collocation
and Galerkin discretizations will be discussed.
Lecture notesThere will be typed lecture notes.
LiteratureLecture Notes.
Prerequisites / NoticeCompleted BSc MATH or equivalent.
401-5650-00LZurich Colloquium in Applied and Computational Mathematics Information 0 credits2KR. Abgrall, R. Alaifari, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab
AbstractResearch colloquium