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# Navier–Stokes equations

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  1. arXiv

    From noisy flow images, blood flow and vessel-wall motion come back together: PirateNets alternation cuts aortic velocity error to 0.0372

    Starting from noisy velocity images, unsteady three-dimensional blood flow and elastic vessel-wall motion can be reconstructed together without a prescribed inlet waveform or initial velocity. The solver alternates a fluid update, in which a physics-informed network fits the observations while enforcing the incompressible Navier–Stokes equations on the moving domain, with a geometry update, in which registration plus interface traction continuity and an elastic momentum residual constrain wall displacement. On a converging channel and a patient-like aorta, the PirateNets version reaches velocity relative errors of 0.0243 and 0.0372, below the 0.1066 and 0.1305 of a standard PINN of the same depth and width.

  2. Nature News

    The Credit Fight in the AI Era: Debate Sparked by OpenAI's Claim on the Navier–Stokes Problem

    A Nature news report says OpenAI announced on 8 September that its AI model solved the Navier–Stokes problem in fluid dynamics and verified the proof using the Lean language, while mathematicians Tristan Buckmaster and Levent Alpöge say they had already been working on the problem with OpenAI and Anthropic tools and Andreas Thom says his discussions about non-sofic groups resembled OpenAI's later approach, prompting an open letter from 25 Fields Medal winners and wider debate about credit and training-data provenance in the AI era.

  3. Nature News

    AI Claims a Navier–Stokes Singularity: What It Means for Fluid Physics

    According to a Nature news report, OpenAI claims its most advanced AI model proved that the Navier–Stokes equations produce a 'singularity' in some instances, predicting physically impossible infinite speeds; the report situates that claim by reviewing the equations' known limits for compressible fluids and rarefied gases, and alternative modelling routes such as the Boltzmann equation, molecular simulation, and a 'triple decker' multiscale coupling.

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