Graduate seminar WS 21/22 Graduate Seminar on Partial Differential Equations
Analysis of Machine Learning Problems: From Theory to Practice
In the past decade, powerful new machine learning methodologies have been developed. The mathematical analysis of these tools is a major challenge, and there is currently still a large gap between theory and practice. In this seminar, selected machine learning methods will be presented and rigorously investigated. Topics are being suggested by a number of different research groups at Bonn. A lot of these approaches rely on tools from functional analysis, approximation theory, calculus of variations and the analysis of partial differential equations, ranging from the rigorous analysis of gradient descent methods and neural network architectures to applications for solving high-dimensional PDEs. In addition, we consider including some talks on the practical implementation of these techniques, and their performance for different applications.