Thank you for the introduction and thank you all for the for coming.

Yeah, so today's talk as the heart mentioned is the something about the intersection of

machine learning and dynamical systems.

So it's in a way it's a survey of different results that have been doing for the last

10 years or so.

So this is joint work between the different people that which are listed in the on this

page.

So, so the main argument here is that the we want to argue that the intersection of

machine learning and dynamical systems is an interesting field I mean that people should

work on and particularly the nice mathematical framework for this intersection would be to

work on in this special kind of Hilbert spaces that are called or producing kind of Hilbert

spaces.

So the general context is how to analyze complex systems and there are essentially one of the

important techniques actually is the to analyze complex systems are either theoretical systems

and machine learning as an approach among others.

So the theoretical systems has been developed since the late 1800s especially through the

efforts of mankind.

It's a model based theory that allows to analyze complex systems when the model is now it offers

many non trivial ways to analyze the systems it has the status of theory but currently

it is limited to low dimensional models and some very particular cases of infinite dimensional

systems.

On the other side we have machine learning that is very popular now and which is a field

that is concerned with algorithms that are designed to accomplish certain tasks whose

performance improves with the input of more data.

So it allows the analysis of some very complex systems and as many of you saw I mean the

systems can be very high dimensional on the basis of their data when and particularly

in case where the model is not even now but there are this field is limited in the sense

that it is a set of techniques and algorithm so the question of reproducibility is not

addressed in the context of machine learning so if one slightly changes the context it's

not clear that a given algorithm will be working.

So there are now clear methodologies the theory is still underdeveloped and it's not clear

why algorithm work and what is their domain of applicability in general.

So it makes sense to combine the systems and machine learning especially in the following

directions.

So the first direction is machine learning for dynamical systems where the goal is to

analyze dynamical systems on the basis of observed data rather than attempt to study

them analytically.

So here this way the goal would be to extend the classical field of dynamical systems to

large dimensional systems for example and the other direction is dynamical systems for

machine learning where the goal here is to analyze algorithms of machine learning using

tools from the field of dynamical systems and here the idea is to look at algorithm

machine learning as dynamical systems themselves that are running on a computer time not time

on the watch but time on the computer which makes algorithm look like a dynamical system.

And so this would give solid foundation to the existing methods and understand their

true potential and limits.

So this I mean I got personally introduced to the field through Steve's mail.

I mean he already mentioned this like many years ago about 15 years ago in the introduction

of the following book, Learning Theory and Approximation Viewpoint where he said that

the unification of dynamical system and learning theory is a major problem and another problem

is to develop comparative study of useful algorithm currently available and to give