I think this is because of all the speakers today and I'm really pleased and happy to

welcome Hubert Klein from the University of Berlin. And before starting, let me make some comments on this interesting

research. Hubert Klein started studying mechanical engineering in Aachen. So first of all, he was an engineer which turned into a kind of

mathematician, I would say. And he did his PhD and also a dissertation with Nobel Prize in Data at Aachen. He did a post-doc in the Kuhn Institute with

And then his first professorship was in Wuppertal. I think not everybody is familiar with this city. And shortly after that he went to Berlin. He had a joint position at the

at the same time at the fine University in Berlin. And now he gave up the position at Bicke and he's now at the fine University in Berlin. He declines a couple of offers from

very prestigious places like ETH in Zurich, Johns Hopkins, and even Princeton. Your comment then was kind of boring. So Berlin at that time was more exciting.

Hubert is also a member of the Berlin-Noranburg Academy and in 2003 he was rewarded with the highest German research prize, the Black Nature Prize. And today, I mean, his field of interest was started with combustion and then he turned to

to meteorology and climatology. But it's inevitable that they come across, say, with machine learning. And today he would like to share some critical view on the current state of machine learning.

So we're very much looking forward to it.

Thank you, Sir. Thank you, Enrico and Eval for the hospitality for inviting me, giving me the opportunity to speak. I'm not a developer of machine learning techniques. I'm not even a user of machine learning techniques. But I've seen in my circles in the black math that more and more people are

jumping on the train and start using this machinery for all sorts of purposes. And some of this has been bugging me. And at some point I thought I should collect my thoughts and whoever doesn't run away when I start talking, I will let them know what I think about the stuff. And now you're my victims.

I will report specifically on results from John Siegler, John Kiley and Zhengchao Xu. Some of you might know Zhengchao. He has made his career in the course of numerical methods of PDEs. He has quite a name there.

But has recently done some work with these postdoc and PhD students that I will refer back to. And the second group I will mention prominently is Ilja Horenko who is now at the Technical University of Kaiserslautern-Landau as a professor for artificial intelligence and a team of postdocs and cooperation partners in the field.

And he is also a professor in bioinformatics and in climate research. I'm very okay. I didn't even mention it.

Okay, so without further ado, I try to get this thing going. Yes. The motivation behind what I'm talking about is from my area of research, atmospheric and ocean flows. And it is about the story of El Nino prediction.

And El Nino is this phenomenon where in the Eastern Pacific, the sea surface temperatures rise strongly around Christmas time. And then the phenomenon holds on for up to two years.

And when the surface is so warm, it has profound effects on the atmosphere, evolution of the atmosphere in the region. And it's so drastic that farmers, in particular in southern South America, they would like to know as long as they, as possible ahead of time whether an animal is coming or not, because it would help them dramatically to buy the right crop, see the right season.

And that's what it means in order to basically cover and counteract the adverse effects of the El Nino. But economically, incredibly important phenomenon too, because of these what is called Taylor connections, the dry rather wet and cool two years we've had around our area here have to do with the presence of an El Nino in this region.

And when the phases change, we will see other weather patterns again over here. So it's actually a global phenomenon. And it turns out that physics based models like weather prediction or climate models have a very hard time predicting accurately.

So the following reason, weather models, weather forecast models are trying to make as good as a prediction as possible for a couple of days. And it is known even theoretically that beyond 10 days, the weather develops its chaotic behavior and the trajectories depart and a precise weather prediction isn't possible anymore, which is why these models are not designed to do more than 10 days.

So if you want to go a couple of months ahead, obviously these models are suboptimal for the purpose. In turn, climate models are made to simulate the statistics of climate. And the definition of climate is the statistical weather over something like 30 years.

So you don't get an answer from climate models for what happens two months ahead. If you run it for 30 years, real time, then you get the statistics of what happens in the 30 years, but you don't get any accurate information of what happened when except for maybe within a season.

And this is why neither the physics based weather nor the physics based climate models are good at doing this kind of seasonal, inter-seasonal, few year predictions.

And that was a motivation for Tom and colleagues to work out a neural network based machine learning based training tool and published in 2019 in Nature.

And what they achieved was to go considerably beyond the 10 months of reasonable, valuable prediction that you can get physics based to 60 months accuracy from just from data.

How did they do that? Basically, you have to know that over the past 60 years, weather services have been recording all the observational data they have been using to do the weather forecasting, and it's also available.

And now what is called a reanalysis nowadays is you take all these data from back then, you take the best available weather forecasting and you run it forward through the decades using data assimilation machinery to basically steer the run as close as possible by the observational record that you have had.

This is the best reconstructions of what happened in the atmosphere in three dimensions that we can nowadays come up with.

And how did I use these data from the three dimensional evolution of the atmosphere from the reanalysis and of course the observations of when did an alineo occur back then to basically train a neural network to say, I give you the data from say,

1965 and I want to know from you, doesn't an alineo occur 60 months later or not? And that was their classification scheme that they tried to train the network for to say, alineo yes or no given conditions sometime earlier.

Okay, this is the background and then my colleagues Ilya Olenko and Trince, they used just as Hamid Al did, sea surface temperatures, but they also used on the suggestion of Terry O'Kane, vertical slice along the equator of ocean reanalysis that Terry had available because he was interested in the question, does the vertical distribution of temperatures and

etc. in the ocean near the equator also have an influence on an alineo evolution? If we knew this well, would it give us predictive scale? That was his science question behind including this data.

So they looked at this vertical gradient of temperature in the slice and the sea surface temperature over here. And of all these fields, Terry had available the alineo distribution.

In these fields, Terry had available the empirical orthogonal functions, the first couple hundred of them, of these distributions.

So if one of you hasn't heard one of the notions, the other they might have. It's basically trying to find out the statistically most important spatial modes, as one says, explain X percent of the statistics over the period.

Okay, this is the data they took, and it's in total 200 degrees of freedom. They took the most important 100 degrees of empirical orthogonal function amplitudes for these two fields.

And then obviously they had the alineo index, which is zero or one depending on the angle there or not. And so this what they actually wanted to learn is a function that goes from R200 to R1.

Constraint is that the number here has to be between zero and one, ideally only zero or one, but that's not what one aims for when it tries to do a probability statement.

And the 200 degrees of freedom are mapped to the probability that the alineo index, as the meteorologists call it, is one or zero.

And the probability the alineo index, that's sort of interesting also just to learn a bit more about the concept. One takes the long term average, 30 year average of sea surface temperatures in the region, and then compares that with the five month average in this region.

And when the deviation between the two is bigger in modulus than 0.4 degrees Celsius, then it's either alineo or linea. When it's hotter, it's alineo, when it's colder, it's linea.

And if it's in between this window of plus or minus 0.4 degrees, it's just normal, nothing.

In reality it's clear whether there's alineo or not.

This is the definition they give. That's all I can say.

And they have good reasons to say it's essentially the same phenomenon, although it varies in amplitude and so on. Anyway, let's see framework.

And now let me dive into...

There's more space up here. If you can read the formulas, please don't hesitate to come up front.

Remarks on high dimensions. So suppose we did for simplicity just 100 degrees of freedom of an input to the function we want to learn.

And we take the measurements of these 100 degrees of freedom every six hours over 30 years, roughly half of the data, which they were training their neural network or EAS machinery with.