With more and more data available for analysis and decision making - from web documents and digital media to sensory data from cameras, microphones, and ubiquitous devices - it becomes increasingly more important to understand how such large volumes of data can be analyzed by computers and used as the basis for new intelligent services, for decision making, and for making computers learn from experience. In companies around the world, from retail and banks all the way to Google, intelligent learning and analysis techniques are used to improve business decisions. Likewise, in science, important discoveries are made easier by automated learning methods, and games and other artifacts are being made adaptive with learning technology.

Within the intelligent systems track of the computer science Master's program, the Algorithms for Data Science course offers in-depth knowledge of different aspects of big data analytics and systems, including algorithmic techniques for analyzing structured and unstructured data that cannot be stored in a single computer because it has enormous size and/or continuously arrives with such a high rate that requires immediate processing. In particular, the topics include classical data mining tasks for massive data and/or data streams, mining massive graphs, and similarity search in massive data.

In this seminar we will study the concept of neural operators, which employ neural networks to learn mappings between infinite dimensional spaces. In practice this means one can train neural networks to e.g. automatically solve entire families of complex partial differential equations, integrate families of functions or infer families of stochastic processes.

Our main goals will be to:

• test these ideas with some simple coding exercises we will do from scratch (In fact, we will empirically demonstrate we can teach a neural network to integrate "any" "nice" function on the real line)
• read and discuss about some current problems of neural operators and their possible solutions
• if we have time we might discuss how to apply the ideas of neural operators to concepts of representation theory

What you will have to do: we will ask you to give two short presentations about some numerical experiments, and hand in a final report

Dates:

• the seminar will run from Monday, February 19, 2024, until March 31 (6 weeks in total).
• Registration (and deregistration) deadline is on: Friday, March 15, 2024
• Preliminary meeting: Monday, February 19, 2024 at 10am in Room 3.110 B-IT