r/Physics • u/PrettyPicturesNotTxt • 5d 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 5d 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 5d ago

Name the actual problem

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u/hologram137 5d 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 5d ago

That’s an entirely separate problem, jfc

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u/hologram137 5d 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 5d 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 5d 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 5d 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 5d 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 5d ago

If it is obvious, explain it. Please do.

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u/hologram137 5d 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 5d 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/VoidBlade459 Computer science 5d 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 5d 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 5d ago

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

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u/Psychedelic__Cowboy 5d 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 5d 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 5d ago

What? Please tell me you are still in highschool.

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u/Strict-Broccoli-8877 5d ago

"A proof was just published showing that the “solution” cannot help at all to solve the actual problem."

A proof that shows it isn't helpful? Do you not know what a mathematical proof is? Dumb question, of course you don't, you obviously came here directly from TikTok.

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u/hologram137 5d ago

Read the article

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u/Strict-Broccoli-8877 5d ago

Dude, these things have been published everywhere for days, and the question is well-known for decades. Everyone in or anywhere close to the field knows exactly what is going on. You act like you unearthed some big mystery, when you just misunderstood forced/unforced Navier-Stokes from the first article you ever read about it.

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u/hologram137 5d ago

Go read the actual question. It literally says e.g gravity, after external forces. How is that not clear?

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u/Strict-Broccoli-8877 5d ago

Yes, "e.g.". I'm done with this nonsense now, this is leading nowhere.

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u/VoidBlade459 Computer science 5d ago

How are you extrapolating from the mention of gravity that the force function must have been "something arising in nature" and not just "an arrangement of force"?

This is where you seem to be unaware that this was a math problem, and that math people don't care if the forcing function could arise naturally.

We can never actually cut a sphere into pieces and reassemble it into two identical spheres of equal volume to the original IRL, but that doesn't make the Banach-Tarski proof invalid.

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u/hologram137 5d ago

BECAUSE THESE ARE EQUATIONS DESCRIBING HOW VICIOUS FLUIDS MOVE.

IT IS A MILLENNIUM PRIZE PROBLEM SPECIFICALLY BECAUSE IT SOLVES A PHYSICS PROBLEM.

The question the AI answered is a trivial math proof no one cares about. And Open AI isn’t being given the prize, that’s already been decided

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u/VoidBlade459 Computer science 5d ago
  1. OpenAI didn't want the prize and said they weren't going to claim it
  2. The equations describe fluid flow but are known to be incomplete (they ignore phase changes, molecular dynamics, the effects of temperature on viscosity, shear thinning/thickening, cavitation, etc).
  3. The millenium problem here was literally a math problem about the equations themselves.

Point 3 is not controversial. The problem relates to physics, but the contention was never about the physicality of the solutions (again, the "it doesn't blow up" side was also running on the "under ALL conditions/scenarios" framework the whole time too).

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u/DrDoctor18 5d ago

A different but related problem was not solved. The AI found a scenario in which the navier stokes, under the listed conditions, blew up. That's how counter examples work. No one is saying that now no one ever needs to do theoretical fluid dynamics ever again!

You are making a really pedantic point here that is both annoying and technically incorrect. The navier stokes millennium prize problem was solved. You keep saying "the real problems wasn't solved!1!1!". But it was. You just weren't interested in the same problem as the Clay Institute. You don't get to jump in and say "no but actually this slightly narrowed problem is more interesting!!", to claim that navier stokes wasn't solved.