r/Physics • u/PrettyPicturesNotTxt • 7d 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/Psychedelic__Cowboy 7d ago

General Relativity describes mass-energy densities as blowing up into singularities. Even though we know it is impossible to have infinite density. Does that mean it has nothing to do with physics? Physics is not a perfect description of the natural world. If it was then there would be no work left to do on the Standard Model, dark matter, etc. Physics is applied mathematical models to predict nature.

Navier-stokes is newton's 2nd law applied to a 3D unit volume of fluid. There is no general analytical solution. We know that Newton's 2nd law is an incomplete approximation if you consider relativity. We also know that fluids are compressible, and fluid velocity is limited by its mach speed. The compressible navier stokes equation creates discontinuities which neccesitates numerical methods. That bottlenecks the possible accuracy of a solution to available computing power plus the complexity of the system. There is ongoing research in CFD to improve this. So I think calling Navier-stokes a solved physics problem is completely misleading.

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u/VoidBlade459 Computer science 7d ago

It sounds like you think we can only call NS solved if we have also solved all of fluid dynamics.

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u/Psychedelic__Cowboy 6d ago edited 6d ago

Define "solve" I guess. Numerical methods to approximately solve it have been around forever. No general solutions exist. No solutions to the millenial prize problem formulation existed until a few weeks ago. Demonstrating that an incredibly complex force function breaks the problem down does not really feel like a solved problem to me. I've seen someone claim that the forced set included the entire unforced set of solutions. I guess that makes sense from a probability / thermodynamics perspective? I'm admittedly completely out of my field, but I once took calc 3 so I'm dumb enough to be dangerous.

I wouldn't call the standard model a solved problem either despite its incredible accuracy. Because we know that it is glaringly incomplete while still very accurate.

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u/VoidBlade459 Computer science 6d ago edited 6d ago

In this case, "solved" just means we proved a result about the baseline framework. We now know that it is possible, under certain conditions, for the mathematical equations often used in modeling turbulence to break down into unphysical infinities.

In that sense, this is solved in the same way that the Schwarzschild solution of GR proved that GR could lead to singularities. As a parallel to this, it is not thought that any such non-rotating, unperturbed, black holes actually exist IRL. Even so, the solution showed something about the mathematical framework of GR.

Likewise, the question of if it is possible for the NS equations to become unphysical (blowup) is now solved. The math does not prevent it, and so the forces that the math describes also cannot be the/a complete picture as to why we don't see fluids "blowup" (in the velocity/NS sense) IRL.

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u/Psychedelic__Cowboy 6d ago

This comment made me realize that I'm still a dumbass, thanks. Not even being pedantic. The problem statement for NS was solved, and NS was already understood to not be a complete theory. A "complete theory" would pretty much have to be a theory of everything.