New in Quanta magazine:

"Latest Neural Nets Solve World’s Hardest Equations Faster Than Ever
Before."

"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."

<https://www.quantamagazine.org/new-neural-networks-solve-hardest-equations-faster-than-ever-20210419/>

At a quick glance, this seems to produce neither symbolic nor numerical solutions.

Martin.

--- SoupGate-Win32 v1.05
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On Tue, 20 Apr 2021 17:27:05 +0200, clicliclic@freenet.de wrote:

New in Quanta magazine:

"Latest Neural Nets Solve WorldÂ’s Hardest Equations Faster Than Ever Before."

"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."

<https://www.quantamagazine.org/new-neural-networks-solve-hardest-

equations-faster-than-ever-20210419/>

At a quick glance, this seems to produce neither symbolic nor numerical solutions.

Which would imply that it solved the equations only for lenient interprations of 'solve'.

--- SoupGate-Win32 v1.05
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On 4/20/2021 9:27 AM, clicliclic@freenet.de wrote:

New in Quanta magazine:

"Latest Neural Nets Solve World’s Hardest Equations Faster Than

Ever

Before."

"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."

<https://www.quantamagazine.org/new-neural-networks-solve-hardest-equations-faster-than-ever-20210419/>

At a quick glance, this seems to produce neither symbolic nor numerical solutions.

Martin,

I'm aware that I could read the article but I simply don't have time at
the moment. So I'm hoping you can fill me in on an aspect of the claim.
First, I'll note that one of the real problems with smart or expert
systems is that most cannot defend or explain their results. So my
question is whether the technology described explains why the solution
is correct and how to derive it or is the user left to try the proposed solution out by substitution in the original or some other such crude
methods? Thanks for any information you might provide.
--
Jeff Barnett

--- SoupGate-Win32 v1.05
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Jeff Barnett schrieb:

On 4/20/2021 9:27 AM, clicliclic@freenet.de wrote:

New in Quanta magazine:

"Latest Neural Nets Solve World’s Hardest Equations Faster Than
Ever Before."

"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."

<https://www.quantamagazine.org/new-neural-networks-solve-hardest-equations-faster-than-ever-20210419/>

At a quick glance, this seems to produce neither symbolic nor
numerical solutions.

I'm aware that I could read the article but I simply don't have time
at the moment. So I'm hoping you can fill me in on an aspect of the
claim. First, I'll note that one of the real problems with smart or
expert systems is that most cannot defend or explain their results.
So my question is whether the technology described explains why the
solution is correct and how to derive it or is the user left to try
the proposed solution out by substitution in the original or some
other such crude methods? Thanks for any information you might
provide.

The "world's hardest equations" are identified as PDEs (the Navier-
Stokes eqation of hydrodynamics being mentioned), and two research
groups are reported to have tackled them by adapting "deep neural
networks". Some of the researchers are mentioned (and pictured), but I
saw no literature references or other pointers to their work. The text
goes on to mention that the neural net serves to approximate the
functional operator defined by a given PDE, and that a Fourier-space
viewpoint is taken by one group.

To me nothing else appears to be worth reporting about the Quanta
article.

Martin.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 4/25/2021 7:47 AM, clicliclic@freenet.de wrote:

Jeff Barnett schrieb:

On 4/20/2021 9:27 AM, clicliclic@freenet.de wrote:

New in Quanta magazine:

"Latest Neural Nets Solve World’s Hardest Equations Faster Than
Ever Before."

"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."

<https://www.quantamagazine.org/new-neural-networks-solve-hardest-equations-faster-than-ever-20210419/>

At a quick glance, this seems to produce neither symbolic nor
numerical solutions.

I'm aware that I could read the article but I simply don't have time
at the moment. So I'm hoping you can fill me in on an aspect of the
claim. First, I'll note that one of the real problems with smart or
expert systems is that most cannot defend or explain their results.
So my question is whether the technology described explains why the
solution is correct and how to derive it or is the user left to try
the proposed solution out by substitution in the original or some
other such crude methods? Thanks for any information you might
provide.

The "world's hardest equations" are identified as PDEs (the Navier-
Stokes eqation of hydrodynamics being mentioned), and two research
groups are reported to have tackled them by adapting "deep neural
networks". Some of the researchers are mentioned (and pictured), but I
saw no literature references or other pointers to their work. The text
goes on to mention that the neural net serves to approximate the
functional operator defined by a given PDE, and that a Fourier-space viewpoint is taken by one group.

To me nothing else appears to be worth reporting about the Quanta
article.

Thanks for the information.
--
Jeff Barnett

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

clicliclic@freenet.de <nobody@nowhere.invalid> wrote:

Jeff Barnett schrieb:

On 4/20/2021 9:27 AM, clicliclic@freenet.de wrote:

New in Quanta magazine:

"Latest Neural Nets Solve World???s Hardest Equations Faster Than
Ever Before."

"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."

<https://www.quantamagazine.org/new-neural-networks-solve-hardest-equations-faster-than-ever-20210419/>

At a quick glance, this seems to produce neither symbolic nor
numerical solutions.

I'm aware that I could read the article but I simply don't have time
at the moment. So I'm hoping you can fill me in on an aspect of the
claim. First, I'll note that one of the real problems with smart or
expert systems is that most cannot defend or explain their results.
So my question is whether the technology described explains why the solution is correct and how to derive it or is the user left to try
the proposed solution out by substitution in the original or some
other such crude methods? Thanks for any information you might
provide.

The "world's hardest equations" are identified as PDEs (the Navier-
Stokes eqation of hydrodynamics being mentioned), and two research
groups are reported to have tackled them by adapting "deep neural
networks". Some of the researchers are mentioned (and pictured), but I
saw no literature references or other pointers to their work.

There are links to two preprints:

https://arxiv.org/abs/1910.03193
https://arxiv.org/abs/2010.08895

--
Waldek Hebisch

--- SoupGate-Win32 v1.05
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On 4/25/2021 3:22 PM, clicliclic@freenet.de wrote:

There are links to two preprints:

https://arxiv.org/abs/1910.03193
https://arxiv.org/abs/2010.08895

Thanks. I missed the links somehow. Let's see what more can be learned
about their approach to PDEs.

Martin.

I was thinking of taking a course in the fall on
Finite elements for solving PDE's.

I am now wondering if I should instead take a course on Neural nets and study AI
instead.

--Nasser

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

antispam@math.uni.wroc.pl schrieb:

clicliclic@freenet.de <nobody@nowhere.invalid> wrote:

Jeff Barnett schrieb:

On 4/20/2021 9:27 AM, clicliclic@freenet.de wrote:

New in Quanta magazine:

"Latest Neural Nets Solve World???s Hardest Equations Faster Than
Ever Before."

"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."

<https://www.quantamagazine.org/new-neural-networks-solve-hardest-equations-faster-than-ever-20210419/>

At a quick glance, this seems to produce neither symbolic nor
numerical solutions.

I'm aware that I could read the article but I simply don't have time
at the moment. So I'm hoping you can fill me in on an aspect of the claim. First, I'll note that one of the real problems with smart or expert systems is that most cannot defend or explain their results.
So my question is whether the technology described explains why the solution is correct and how to derive it or is the user left to try
the proposed solution out by substitution in the original or some
other such crude methods? Thanks for any information you might
provide.

The "world's hardest equations" are identified as PDEs (the Navier-
Stokes eqation of hydrodynamics being mentioned), and two research
groups are reported to have tackled them by adapting "deep neural networks". Some of the researchers are mentioned (and pictured), but I
saw no literature references or other pointers to their work.

There are links to two preprints:

https://arxiv.org/abs/1910.03193
https://arxiv.org/abs/2010.08895

Thanks. I missed the links somehow. Let's see what more can be learned
about their approach to PDEs.

Martin.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

"Nasser M. Abbasi" schrieb:

On 4/25/2021 3:22 PM, clicliclic@freenet.de wrote:

There are links to two preprints:

https://arxiv.org/abs/1910.03193
https://arxiv.org/abs/2010.08895

Thanks. I missed the links somehow. Let's see what more can be
learned about their approach to PDEs.

I was thinking of taking a course in the fall on
Finite elements for solving PDE's.

I am now wondering if I should instead take a course on Neural nets
and study AI instead.

As far as I can see, the neural nets here serve to interpolate between
a large collection of numerical solutions to a given PDE, which have to
be computed first by some other method.

So this method must be considered numerical, and Finite Elements won't
become obsolete soon. The neural net, however, can apparently overcome
the "curse of dimensionality" that besets interpolation in general.

While the interpolation may be "blazingly fast", the computation of
numerous reference solutions will remain slow as always.

Martin.

--- SoupGate-Win32 v1.05
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On Wednesday, 21 April 2021 at 01:22:02 UTC+10, nob...@nowhere.invalid wrote:

New in Quanta magazine:

"Latest Neural Nets Solve World’s Hardest Equations Faster Than Ever Before."

Can Neural Nets solve fractional partial differential eq?

http://drhuang.com/science/mathematics/fractional_calculus/fractional_differential_equation.htm

mathHand.com can.

--- SoupGate-Win32 v1.05
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