PDEs cracked by Artificial Intelligence at Cal Tech

[Tom.G]

With a 1000 time speed-up too, this could be a game-changer.

From: https://www.technologyreview.com/20...er-stokes-and-partial-differential-equations/

They did it by solving in "...Fourier space (rather) than to wrangle with PDEs in Euclidean space, which greatly simplifies the neural network’s job.

...capable of solving entire families of PDEs—such as the Navier-Stokes equation for any type of fluid—without needing retraining. Finally, it is 1,000 times faster than traditional mathematical formulas...

The full paper from The California Institute of Technology:
https://arxiv.org/pdf/2010.08895.pdf

Cheers,
Tom

 

[jedishrfu]

Interesting notion. The Eureqa software used extensive data and a genetic algorithm to discern the equations of motion of a compound pendulum.

This AI system uses the images to identify the equation's form and then goes from there.

 

[LieToMe]

I couldn't help but notice the lack of an explicit formula for the equations. Did an AI actually solve them or just approximate the solution implicitly on its own?

 

[nsaspook]

IMO it's not really "AI". It is function approximation, there is nothing intelligent about it. The natural intelligence of the researchers is real.

 

[LieToMe]

Seems AI have trouble with math proofs atm, but if they can predict chaotic behavior better than people can it's still a significant step. The same issue occurs in medicine where doctors aren't given information by AI as to how it recognizes cancer and heart disease sooner than they can.