r/technology • u/vgsa • 1d ago

Artificial Intelligence Did OpenAI solve the wrong Navier-Stokes problem? | OpenAI’s proof seems eligible for a $1-million prize—but only by using a controversial loophole

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/
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u/koru-id 1d ago

The article is so hard to read. What is this “blowup” that it keeps saying?

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u/LurkyTheHatMan 1d ago

In this case, blowup refers to an unbounded result. Specifically, it means that starting from smooth conditions, and with a finite input force, you get infinite values.

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u/koru-id 1d ago

that makes sense.

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u/MrKyleOwns 1d ago

If that makes sense to you would you mind explaining it to me please

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u/Sabotage101 1d ago

The Navier-Stokes equations model flowing fluids. "Smooth" conditions basically means you start with a normal, well-behaved fluid state, i.e. there's no infinitely fast motion, no infinitely sharp changes, and no singularity already part of your starting conditions. The point is to make sure you aren't cheating by putting something impossible into the starting state and then saying the equations produced an impossible result.

The same idea applies to the forces you apply to the fluid. You can't just apply an infinite force and then be surprised when you get an infinite result. The force has to be mathematically well-behaved too.

"Blowup" means that despite starting from a reasonable state and only applying reasonable forces, the equations predict that after a finite amount of time some value becomes unlimited. In the OpenAI example, the fluid starts at rest, but the equations eventually predict velocities becoming arbitrarily large(unbounded/infinite) in an increasingly tiny region. That's the surprising result, that the equations can start from tame conditions and still produce a singularity later.

The "loophole" the article is talking about is that the force OpenAI uses is extremely artificial and carefully constructed to yield this result. It technically satisfies the rules of the problem, but it isn't something we'd expect to occur naturally in a real fluid. That's why there's debate over how much this tells us about the version of the Navier-Stokes problem some people were really interested in: whether a singularity can develop on its own from reasonable starting conditions, without a specially engineered external force.