We are pleased to announce the first mini-course in 2022 dedicated to the hot and broad topic of Machine Learning, more details to be found below.

Title: Data-driven modeling and optimization of dynamical systems under uncertainty

Lecturers: Jia-Jie Zhu (WIAS Berlin) & Feliks Nüske (MPI Magdeburg)

Dates & Times: Monday, 11 July to Thursday, 14 July, 1pm to 5pm

Location: MA 748, TU Maths Building

Abstract:

Machine learning (ML), including deep learning and reinforcement learning, has become a powerful tool for modern science from various disciplines. Beyond traditional supervised and unsupervised learning, an important current topic is data-driven modeling and decision-making in dynamical systems. This mini-course will explore two important aspects: modeling and decision-making (optimization), of dynamical systems driven by ordinary or stochastic differential equations.

In the first part, we will learn about Koopman theory, which is one of the most widely used frameworks for the data-driven analysis of dynamical systems. We will explore the basic theory, the resulting numerical methods, and how these methods can be utilized towards analysis, model reduction, and forecasting of the system at hand.

In the second part, we will explore the decision-making aspect, where we will introduce principled mathematical optimization and control. We then highlight those principles and tools in popular modern learning models such as kernel methods and neural networks. We will pay special attention to a pressing issue in ML applications, which is the lack of robustness and safety in decision-making, and present the guiding principles and modern strategies to improve the robustness and reliability of learning and decision-making systems.