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Comment by newprint | Hacker News Reader

Why AI is needed for Fluid dynamics ?

"perfectly correct" fluids are crazy computationally intensive. However if you can fake it with "close enough" fluids, they still look perfect, but take a fraction of the computation.

Don't use them for wave slam on a vessel, but they're brilliant for games.

I was hoping for CFD applications myself when I saw the headline... Is there any progress on that direction or is it even possible?

there’s tons of research in that general direction. not sure if any is practically better yet but it does “work”.

look up Nvidia modulus.

Check out Navier Stokes and Partial Differential Equations.

Reading through some SIGGRAPH papers on fluid dynamics might be interesting.

The TLDR is that fluid dynamics can't be efficiently calculated exactly, and the computational complexity grows exponentially for linear improvements in fidelity.

AI simulations can generate natural seeming fluids in constant amounts of compute, by learning heuristics that look realistic but may not actually exactly match what you'd get from running a PDE solver.

Who said that neural networks can't approximate solutions to these equations with any accuracy / precision we like?

In theory, they can (Universal approximation theorem ). But those spatio-temporal systems are highly complex and consist of a very big number of variables (curse of dimensionality). That's part of why weather forecasting is so hard.

So, to not have to use a gigantic neural network at the problem, you use some clever 'tricks', like dimensionality reduction and decomposing the problem. For example you can separate the spacial domain from the time domain and predict those with dedicated models, before joining the solutions again.

Is the number of variables really big or is it because no one ever tried large models with billions of parameters for this purpose (too expensive) like it was done with GPT?

The number is really big. GPT uses Transformers, which are kind of the successor to RNNs. Both are good at modelling sequences, like sentences or the temporal evolution of a dynamical system.

It look like something GPT wrote.

There are 3 spacial dimensions + one time dimension in Navier-Stokes equations. Not billions.

Lol, i guess we'll hear this allegation more often in the future. I'm talking about 3 variables for the velocity and 1 variable for the pressure at every point in space(typically a cartesian grid in numerical fluid simulation) and every time step of the solution.

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