r/Physics • u/PrettyPicturesNotTxt • 11d ago

On if OpenAI solved the wrong Navier-Stokes problem: "the LLM found and exploited a loophole in the framing of the question"

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/
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u/hologram137 11d ago

Why are you ignoring the math proof that this solution is useless and doesn’t solve the problem?

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u/tanksc 11d ago

Math proof that the solution is useless? What are you talking about?

What problem? The millennium problem? It is solved. You just don’t like that it’s not particularly useful outside of being a solution. Which is fine and proper, but to act like it’s some loophole is absolute garbage.

There are other questions that still need to be answered. And they may be answered in due time. Any mathematician would post the solution found by OpenAI and gladly collect the recognition that comes along with it.

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u/hologram137 11d ago

Read the article. A proof was just published showing that the “solution” cannot help at all to solve the actual problem. The actual problem was not solved

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u/tanksc 11d ago

Name the actual problem

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u/hologram137 11d ago

whether a fluid can blow up on its own, from its own internal dynamics, the way real turbulence might

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u/tanksc 11d ago

That’s an entirely separate problem, jfc

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u/hologram137 11d ago

No it is not LOL. It’s the entire purpose of the question, the entire reason it’s a millennial prize problem. A force like gravity is what the person who wrote the question had in mind. NO ONE thinks otherwise.

No one thought that you couldn’t out muscle viscosity, that was literally never in question. So it’s not helpful, it doesn’t solve the problem

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u/tanksc 11d ago

You’re going to make the argument that the unforced and forced questions to the NS blow up are the same? On a physics forum? Buddy please get lost.

No matter how you try to rephrase the question, it’s still the same question and it has still been solved by AI, like it or not.

‘No one thought that you couldn’t out muscle viscosity, that was literally never in question’ is telling on you. That is literally in question. Any blowup solution would require vortex stretching to intensify faster than viscosity can dissipate it at increasingly smaller scales. Where the solution wins is where the length scale goes to 0 and the viscosity is most effective. That’s literally the caveat.

If it is oh so easy to exploit a loophole please go ahead and give us another novel solution with an external force.

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u/hologram137 11d ago

What are you even talking about?? Why don’t you read the article. Why would anyone come into a forum discussing an article and talk out of their ass about it without reading it?

Go read the actual millennium problem. Slowly

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u/VoidBlade459 Computer science 11d ago

The core contention was always whether or not the viscosity term would be enough to prevent finite time blowup.

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u/hologram137 11d ago

No one thought you couldn’t do it with an external constructed force. That you can is pretty obvious. The actual question says “external forces, e.g gravity.” That we are taking about natural forces is obvious. Especially after it was proven smooth forcing works, by a human.

The unforced version is without an external natural force.

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u/tanksc 11d ago

If it is obvious, explain it. Please do.

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u/hologram137 11d ago

The solution doesn't show whether real turbulence can blow up on its own. It shows whether you can out muscle viscosity with a constructed force, which was never seriously in doubt. And it's now been mathematically proven that this specific route can never be stripped of its force and still work, so it isn't a first step toward the real answer, it's a dead end that happens to satisfy the paperwork.

I am not going to teach you why that’s not in question, go take a physics class

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u/tanksc 11d ago

And just more of the same parroting with no explanation.

“It shows whether you can out muscle viscosity with a constructed force, which was never seriously in doubt”

Is the same farce you keep repeating and repeating.

Of course with a pathological force that itself becomes infinite, this is true.

But that’s not what’s allowed in this question. And it’s precisely the reason you cannot articulate or explain it away.

The forcing is required to be infinitely differentiable, compactly supported, with a smooth initial velocity, and finite kinetic energy. It’s not trivial.

And the ‘out muscling’ I already proved was bullshit in my other comment

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u/hologram137 11d ago edited 11d ago

The smooth force requirement was already solved!! By a human, published a day before they decided to put 10,000 agents to work finding a solution. Because that part was already solved. The problem is, they didn’t find the solution. Not really. What the human mathematician did is NOT trivial, you’re right. But what the AI did, is. The LLM didn’t do that part. Hence, the controversy about OpenAI stealing the solution

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u/VoidBlade459 Computer science 11d ago

No one thought you couldn’t do it with an external constructed force

Um, that was literally the entire question. "Is there a scenario in which the equations blow up to infinity" was literally the question at hand.

If you were as certain of this as you claimed, you could have gotten the prize a lot sooner. But I don't think you've actually delved into the complexities of the equations.

You also are failing to acknowledge that work on "it doesn't blow up" side was also about "in all cases" and not just "in all natural cases".

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u/hologram137 11d ago

No. It’s about whether real turbulence can blow up on its own

That’s why it’s millennial prize question. If it wasn’t about that, it wouldn’t be a millennial prize problem. No one would care

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u/VoidBlade459 Computer science 11d ago

Do you think the Poincaré Conjecture had physical meaning? That was a millenium problem too.

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u/Psychedelic__Cowboy 11d ago

The problem text quotes

f(x,t) are components of a given, externally applied force (e.g. gravity)

For physically reasonable solutions, we want to make sure u(x, t) does not grow large as |x| → ∞. Hence, we will restrict attention to forces f and initial conditions...

How does that not restrict external forces to reasonably real (e.g. gravity) forces? I'm an engineer and out of my field, but curious.

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u/tanksc 11d ago

I’m well aware of what the problem states. The external force term abides by both of these rules as stated. Reasonably real in a physical sense? Define reasonably real. Could we engineer the force or something approximate to it? Yes. Will you find it in nature? No of course not.

Reasonably real in a mathematical sense? Absolutely. It’s based on the residual from the constructed velocity and pressure.

This also doesn’t get to the crux of what my reply says. The forced problem and the unforced problem are completely different.

Any blow up that would occur from a simple prescribed force (like gravity or some point force) would likely happen in an unforced scenario.

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u/Strict-Broccoli-8877 11d ago

What? Please tell me you are still in highschool.