Our next speaker in the series of more Mathematics of Data Center lectures.

So today we have the great pleasure of having with us Sebastian Pikes.

So you see he's a young but still as you will see extremely prolific scientist.

He got a bachelor and a master in Athens.

He has been since then in Paderborn University where he has been a junior professor.

Recently he got an offer that he accepted to become a full professor at the Technical University of Dortmund,

where you can meet him starting in next October.

So congratulations for all these achievements.

And his recent work has been very much on the interface between control sciences and machine learning.

And yeah, I think it was maybe I don't know how I got to know about his work,

but I found it particularly interesting with some substantial connections with some of the topics that we are working in in our group as well.

So I thought that it would be a great lecture to listen.

And Sebastian was kind enough to accept and come visit us for the occasion.

So now is your time.

OK, thank you.

Thanks a lot, Enrique, for the kind introduction and also the invitation.

It's a very great pleasure to be here.

Yes, and this is a rather lengthy title, but maybe we can jump over this and dive right into what I want to do.

So my overarching goal in my research is to study complex systems, mostly governed by partial differential equations.

So potential applications, fluid mechanics, aerodynamics.

Starting to look into physics, the magneto hydrodynamics, where you have even more complex physics or really been our connection,

where you have these buoyancy driven flows.

So all of these systems are governed by PDEs.

So state is dependent on space and time.

And standard numerical discretization schemes like finite elements, finite difference can usually be used,

and they are super accurate and also efficient by modern standards.

But still, if the complexity becomes this high, then they tend to be very expensive to simulate.

We need high performance computing and topics like this to do so.

And even more problematic is this if we want to use the model several times,

and determining feedback laws or solving optimization problems.

So classical multi-query context.

So this is true for two topics that I would like to cover today,

which is the control case using model predictive control on the one hand.

So I'm using a model to solve an optimization problem online and reinforcement learning,

where I try to train an agent that learns by trial and error with the system how to optimally influence it.

And so the aim, since these are so expensive, is to exploit structure in the system to learn models or learn control laws in a more efficient manner.

And what I mean by structures is something I'm going to talk about in quite a bit of detail.

Structure also means I can use a learning algorithm that specifically is tailored to dynamics.

This would be a simple structure.

I know that I'm dealing with dynamic systems, but we're also going to talk a little bit about symmetries.

And I use additional knowledge on my system that it is even more efficient to solve it or to solve the learning problem.

And I use these models further on.

OK, so but before we dive in, it's very cool that I'm in Erlang and particularly in the Felix Klein building.

And so a small reference here, there's a very popular area of machine learning nowadays that is called geometric deep learning.

And so the authors of this, it's a book, not yet published, but it's rather substantial book about this topic.

And they argue that they have been heavily influenced by Felix Klein and his idea of using symmetry as a tool.

A concept for many branches of mathematics.

And they don't claim to make equally substantial contributions, but they say that they have been heavily inspired by this mindset.

To use symmetry concepts in connection with machine learning to show that, you know, actually symmetries play a vital role in many areas of learning as well.

And so I find this really cool because of the location, but also to see that this is something that is rather old,