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The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.
For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.
A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.
Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster.
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