## Christoph Schwab: Catalogue data in Autumn Semester 2017 |

Name | Prof. Dr. Christoph Schwab |

Field | Mathematik |

Address | Seminar für Angewandte Mathematik ETH Zürich, HG G 57.1 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 35 95 |

Fax | +41 44 632 10 85 |

christoph.schwab@sam.math.ethz.ch | |

URL | http://www.sam.math.ethz.ch/~schwab |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-3650-67L | Numerical Analysis Seminar: Tensor Numerics and Deep Neural Networks Number of participants limited to 10. | 4 credits | 2S | C. Schwab | |

Abstract | The 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. | ||||

Objective | The 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 https://sinews.siam.org/Details-Page/deep-deep-trouble Numerical experiments will be done with TENSORFLOW and with the TT toolbox at https://github.com/oseledets/TT-Toolbox | ||||

Lecture notes | The seminar will study a set of 10 orginial papers from 2015 to today. | ||||

Literature | Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen Optimal Approximation with Sparsely Connected Deep Neural Networks arXiv:1705.01714 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, arXiv:1705.02302v3. 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 / Notice | Completed BSc MATH exam. | ||||

401-4645-67L | Numerics for Computational Uncertainty Quantification | 10 credits | 3V + 2U | C. Schwab | |

Abstract | The 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. | ||||

Objective | The 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 notes | There will be typed lecture notes. | ||||

Literature | Lecture Notes. | ||||

Prerequisites / Notice | Completed BSc MATH or equivalent. | ||||

401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics | 0 credits | 2K | R. Abgrall, R. Alaifari, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab | |

Abstract | Research colloquium | ||||

Objective |