[x3d-public] Deep Learning AI solves PDEs and Navier-Stokes in Fourier space

[John Carlson]

Just click away from the "subscribe" window.  You don't have to give
credentials, AFAIK.

I agree one must compare against reality!  Isn't that what wind tunnels are
for?

I think the main point is, we can save a ton of supercomputer time, once
the networks are trained.

I forgot to put "solve" in quotes as the article did.  Important
difference!   Thanks!

Hmm.  I know that a generative adversarial network (GAN) can drastically
improve the results from a neural network.  My guess is that the deep
learning system has a way of testing the "solution."   So you have one
neural network generating the "solution," and one saying if the "solution"
is good or not.  I am not sure if something like that was used here or
not.  My guess is one must read the paper behind the article.

John

On Thu, Nov 12, 2020 at 4:12 AM Don Brutzman <brutzman at nps.edu> wrote:

> On 11/11/2020 11:36 PM, John Carlson wrote:
> >
> https://www.technologyreview.com/2020/10/30/1011435/ai-fourier-neural-network-cracks-navier-stokes-and-partial-differential-equations
>
> neural nets cannot "solve" partial differential equations.  a complex NN
> surface might approximate a mathematical surface but has no way to tell you
> when it's pattern matching attempts are incorrect.
>
> adapting a quote from Richard Hamming: i have no desire to fly in an
> airplane that depends on such solutions to remain airborne.
>
> btw MIT Tech Review apparently wants personal information before reading.
> no thanks.
>
> > Can we subclass VolumeRendering API to include solutions for
> Navier-Stokes PDEs?
>
> no.  but an application might use any part of X3D to visualize any kind of
> solution for such partial differential equations.
>
> > Is this something d3-x3d is interested in?  James?
>
> another worthy path forward would be encouraging the major math programs
> (Mathworks et al.) to continue improving their X3D export.
>
> thanks John.
>
> all the best, Don
> --
> Don Brutzman  Naval Postgraduate School, Code USW/Br
> brutzman at nps.edu
> Watkins 270,  MOVES Institute, Monterey CA 93943-5000 USA   +1.831.656.2149
> X3D graphics, virtual worlds, navy robotics
> http://faculty.nps.edu/brutzman
>
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