Thank you very much for the introduction

Enrique.

Yes, I studied here.

It's great to be back.

I have a reason to come back to Erlangen.

I finished my PhD in 2007, so it's been a while.

This room did not exist back then.

I want to talk about what I summarized here in the title as AI components in PDE solvers.

And then I noticed...

Oh, right.

Spoilers already.

Yes, exactly.

It's actually potentially a good keyword that summarizes the topic are those differentiable

solvers in the subscript here.

Those are actually playing the key role, but I'll explain in a moment how those two play

together.

Yeah.

Let me start very broadly.

So we're dealing with PDEs, with physical systems.

PDEs basically give us a language to work with and model

and ideally also understand

what happens in nature around us.

So in my group, we are often working with fluids.

As you can already see here, the air in this room, right, you don't see it, but it actually

has a very complicated motion.

It's more obvious if you look at liquids

actually two-phase flow right here

water

and air.

We usually see it from the air, so we look at the water.

But Navier-Stokes underneath is a very similar and unifying description of it

or it's also

an important topic.

It keeps the airplane upright.

Lift and drag are very classic themes for transportation and play a role in many real

world applications.

Now we have these AI technologies, and it used to be necessary to motivate why it is

worth looking at it all and whether in the context of if we have a physical model, whether

that makes sense and so on.

By now

I think touring and Nobel prizes indicate there is something that's worth looking at

at least.

So there are definitely many open questions

but it's pretty established by now that it's

a pretty powerful technology that is worth considering.

And the general kind of theme and goal with this combination is

of course

we have these

PDEs.

We have a lot of classic tools to solve them.