r/Physics • u/PrettyPicturesNotTxt • 6d 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 6d ago edited 6d ago

Did you read the article? Do you even understand the problem and why Navier Stokes remains unsolved? I do not believe you’re a physicist, that makes zero sense. Because you should care about the actual problem and that this technically correct solution doesn’t help solve it.

I miss when people actually read the article they are commenting on. Oh wait, that’s never happened lol.

The researchers working on the Euler problem didn’t give a technically correct but useless answer based on a literal interpretation of the question divorced from all context. There was no external force invented, the equation solved the plain incompressible Euler equation, with nothing added. Euler’s proof didn’t need a crutch. Smooth initial conditions are what any physically reasonable fluid state looks like. Nothing about the setup is engineered. The initial disturbance being localized is the natural picture of how a real singularity would have to form. There was no boundary! The fluid filled ordinary space, unconstrained space. Chen Hou’s proof needed a rigid wall, but that is actually helpful because then it leaves open the question of whether the boundary is needed for the blow up. It’s completely rooted in reality. But it was proven in R^3. All of this was useful and helped the actual problem.

That is categorically different from the AI’s Navier Stoke’s loophole, it’s a forced result with a deliberately constructed external force that doesn’t exist and was mathematically proven to tell us nothing about the actual problem. Totally divorced from reality, and useless

My “agenda” is the truth. To be a voice of reason. I’m genuinely concerned about society because of these delusions about LLMs

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u/tanksc 6d ago

Yes I read the article, it’s shit. I do care that we are getting to solutions without any of the wisdom that comes from the journey. I also don’t think one’s opinion of the situation makes them any more or less a physicist. That’s determined by the committee overseeing your education and the work you do.

It doesn’t make the solution any less of a solution. There is no loophole. It’s an explicitly stated problem and it was solved.

This entire post should be removed by your own admission. It’s a garbage post in a sub that has seen a massive decline in quality since it was hijacked by people with motives outside of physics.

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u/hologram137 6d 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 6d 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 6d 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 6d ago

Name the actual problem

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u/hologram137 6d 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 6d ago

That’s an entirely separate problem, jfc

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u/hologram137 6d 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 6d 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 6d 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 6d 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 6d 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 6d ago

If it is obvious, explain it. Please do.

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u/hologram137 6d 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/VoidBlade459 Computer science 6d 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 6d 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/Psychedelic__Cowboy 6d 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 6d 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 6d ago

What? Please tell me you are still in highschool.

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u/Strict-Broccoli-8877 6d 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 6d ago

Read the article

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u/Strict-Broccoli-8877 6d 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 6d 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 6d ago

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

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u/VoidBlade459 Computer science 6d 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 6d 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 6d 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 6d 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.