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Gradient flows SemesterSoSe 2024 Lecturer Tim Laux Type of course (Veranstaltungsart) Vorlesung German title Gradient flows Contents A large variety of dynamical problems are gradient flows, which means they can be viewed as the steepest descent in an energy landscape. These problems are ubiquitous in our physical world, but also human-made systems are based on this principle: Gradient flows are the workhorse of today's machine learning algorithms. After an introduction in the finite-dimensional setting (giving rise to systems of ordinary differential equations), this course builds up the general theory for gradient flows. Then we will address a selection of problems from physics and data science that can (almost) be put into this abstract framework. Along the way, we will also familiarize ourselves with basic themes of modern analysis like Gamma-convergence and some aspects of optimal transport. Literature Lecture notes will be provided. Additionally, some parts of the following references will be useful: • L. Ambrosio, N. Gigli, G. Savaré. Gradient flows in metric spaces and in the space of probability measures. Springer, 2005. • Villani, Cédric. Topics in optimal transportation. American Mathematical Society, 2003. • Mielke. An introduction to the analysis of gradient systems. https://arxiv.org/abs/2306.05026 Recommended previous knowledge Functional Analysis, Analysis I-III, Linear Algebra I Time/Date Mo u. Do jeweils 10-12 Uhr Location M102 Registration
The course consists of 3 hour lectures and 1 hour exercise classes (biweekly exercise classes of 2 hours Modules MV, MAngAn, PHY-B-WE3, PHY-M-VE3, CS-B-Math4, CS-M-P1,CS-M-P2, CS-M-P3 ECTS 6 |