Can someone explain to me? What does it mean to "solve" Navier-Stokes? It's a PDE so it doesn't have a solution unless you apply it to a specific system.

@Touick People are usually speaking imprecisely, and what they really mean is to solve the "Navier-Stokes existence and smoothness problem", as defined in the Millennium Prize Problems: (or something equivalent)

Prove or give a counter-example of the following statement:

In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.

@retr0id Thank you for the explaination, it makes more sense now.

A good question could be if anything impossible happens either way. If for example solving it allows for over-unity, or some parts of a fluid to travel backwards in time, or the energy somewhere to be infinite. We can start by assuming some things are impossible and then work backwards to rule out some possible answers.

big subsidy!! ty manifold

will give my left hoof if this resolves yes. google’s approach might help uncover behavior of some of the remaining singularities, but ultimately the only way we’re seeing a YES is if these additional PINN-ansatz singularities paint enough of a picture to show complete nonexistence of finite-time singularities in the next year, which is a wild assertion.

on top of this, while the findings in the paper are interesting, iterative application of NN ansatzes to PDEs is nothing new—this has been a known technique used in ML for computational chemistry for over a decade now. respectfully feels like this was more a marketing stunt than anything.

(love you all, be nice to forest animals and spread kindness wherever you are!)

@fluttershy no you're right they're never solving this and everyone is dumb !!!!

@strutheo im a honse,

Heheheheheh wtf

Shocking how much news gets broken on prediction markets these days

subsidized