course: 2AMM40

The goal of the course is to teach you skills for building advanced data-driven methods for accelerating scientific discovery. Traditional Machine Learning (ML) and Deep Learning (DL) methods excel at pattern recognition in static datasets. However, the physical world is dynamic, complex, and governed by strict physical laws. By building on your core knowledge of ML, DL, and generative modeling, this course introduces you to the necessary knowledge for modeling complex real-world dynamical systems such as weather forecasting, protein folding and modeling the spread of infectious diseases. 

Dynamical systems provide the mathematical framework for describing how a system’s state evolves over time. In scientific and engineering contexts, these systems often feature high-dimensional state spaces and intricate geometries. In this course we study these challenges through three primary areas of focus:

• Autoregressive Modeling: You will learn how to model systems that change over time and understand how to deal with model stability and accumulation of errors. 
• Geometric Deep Learning: You will learn to exploit the complex geometries of physical data and their corresponding data domains such as geometric graphs, meshes, and grids. You will learn about geometric symmetries and how to incorporate them into your neural network architectures. 
• Probabilistic Modeling: Many scientific phenomena are highly sensitive to initial conditions, where microscopic changes can cause trajectory divergence. You will explore state-of-the-art probabilistic modeling methods such as diffusion models to quantify uncertainty and deal with bifurcations.

The course includes theoretical and practical aspects. The assessment is planned with a practical assignment that involves a report and presentation.  Plenary lectures cover the theoretical aspects, practical sessions, cover instructions and consultations sessions giving students the opportunity to receive feedback on the assignment progress. 

Details

Level:

Master

Quartile:

Q1

Lecturers:

Vlado Menkovski