Winter Semester 2020/21

Multilevel Strategies for Non-Linear Problems and Machine Learning: On Non-Linear Preconditioning, Multilevel Optimization, and Multilevel Training.

Jan 5, 2021 15:00
Jan 7, 2021 15:00
Jan 12, 2021 15:00
Jan 14, 2021 15:00

In this lecture series, we will discuss the main ideas of multilevel optimization techniques and their relation to classical multigrid theory. We will discuss how multilevel optimization methods for convex and non-convex minimization problems can be constructed and analyzed. We will study the significant gain in convergence speed, which can be achieved by multilevel minimization techniques.

Multilevel optimization techniques are also intimately linked to non-linear preconditioning. As it turns out, the minimization-based view on non-linear problems can not only help to design efficient preconditioners, but is also useful for the construction of globalization strategies.

In the last part of the lecture series, we will employ multilevel optimization techniques in the context of machine learning and will discuss their benefits for the training of neural networks. Various numerical examples from phase field models for fracture, from non-linear elasticity, cardiac simulation, and from deep learning will illustrate our findings.“

Rolf Krause is the Chair for Advanced Scientific Computing and Director of the Institute of Computational Science of the Faculty of Informatics at the Università della Svizzera Italiana (USI), in Lugano, Switzerland. His scientific research focuses on numerical simulation and mathematical modeling in scientific computing and computational sciences. In his scientific work, Rolf Krause focuses on multiscale and multilevel solution and optimization methods for the numerical solution of coupled partial differential equation (PDE) systems with applications in uncertainty quantification, (contact) mechanics, medicine, and geology.

MATH+ Thematic Einstein Semester on Energy-based mathematical methods for reactive multiphase flows
Kick-off Conference: 26-30 October 2020
Student Compact Course: 12-23 October 2020
TES Final Conference: 22-26 February 2021