Solve PDEs...

S

Steve Wilson

Guest
Oct 30, 2020

AI Has Cracked a Key Mathematical Puzzle For Understanding Our World

Posted by msmash on Friday October 30, 2020 @01:26PM from the
closer-look dept.

An anonymous reader shares a report:

Unless you\'re a physicist or an engineer, there really isn\'t much
reason for you to know about partial differential equations. I know.

After years of poring over them in undergrad while studying
mechanical engineering, I\'ve never used them since in the real
world. But partial differential equations, or PDEs, are also kind of
magical. They\'re a category of math equations that are really good
at describing change over space and time, and thus very handy for
describing the physical phenomena in our universe. They can be used
to model everything from planetary orbits to plate tectonics to the
air turbulence that disturbs a flight, which in turn allows us to do
practical things like predict seismic activity and design safe
planes. The catch is PDEs are notoriously hard to solve. And here,
the meaning of \"solve\" is perhaps best illustrated by an example.

Say you are trying to simulate air turbulence to test a new plane
design. There is a known PDE called Navier-Stokes that is used to
describe the motion of any fluid. \"Solving\" Navier-Stokes allows you
to take a snapshot of the air\'s motion (a.k.a. wind conditions) at
any point in time and model how it will continue to move, or how it
was moving before.

These calculations are highly complex and computationally intensive,
which is why disciplines that use a lot of PDEs often rely on
supercomputers to do the math. It\'s also why the AI field has taken
a special interest in these equations. If we could use deep learning
to speed up the process of solving them, it could do a whole lot of
good for scientific inquiry and engineering.

Now researchers at Caltech have introduced a new deep-learning
technique for solving PDEs that is dramatically more accurate than
deep-learning methods developed previously. It\'s also much more
generalizable, 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, which would ease our reliance on
supercomputers and increase our computational capacity to model even
bigger problems. That\'s right.

Bring it on.

<https://tech.slashdot.org/story/20/10/30/1727201/ai-has-cracked-a-key-
mathematical-puzzle-for-understanding-our-world>


--
Science teaches us to trust. - sw
 
On Friday, October 30, 2020 at 2:34:22 PM UTC-4, Steve Wilson wrote:
Oct 30, 2020

AI Has Cracked a Key Mathematical Puzzle For Understanding Our World

Posted by msmash on Friday October 30, 2020 @01:26PM from the
closer-look dept.

An anonymous reader shares a report:

Unless you\'re a physicist or an engineer, there really isn\'t much
reason for you to know about partial differential equations. I know.

After years of poring over them in undergrad while studying
mechanical engineering, I\'ve never used them since in the real
world. But partial differential equations, or PDEs, are also kind of
magical. They\'re a category of math equations that are really good
at describing change over space and time, and thus very handy for
describing the physical phenomena in our universe. They can be used
to model everything from planetary orbits to plate tectonics to the
air turbulence that disturbs a flight, which in turn allows us to do
practical things like predict seismic activity and design safe
planes. The catch is PDEs are notoriously hard to solve. And here,
the meaning of \"solve\" is perhaps best illustrated by an example.

Say you are trying to simulate air turbulence to test a new plane
design. There is a known PDE called Navier-Stokes that is used to
describe the motion of any fluid. \"Solving\" Navier-Stokes allows you
to take a snapshot of the air\'s motion (a.k.a. wind conditions) at
any point in time and model how it will continue to move, or how it
was moving before.

These calculations are highly complex and computationally intensive,
which is why disciplines that use a lot of PDEs often rely on
supercomputers to do the math. It\'s also why the AI field has taken
a special interest in these equations. If we could use deep learning
to speed up the process of solving them, it could do a whole lot of
good for scientific inquiry and engineering.

Now researchers at Caltech have introduced a new deep-learning
technique for solving PDEs that is dramatically more accurate than
deep-learning methods developed previously. It\'s also much more
generalizable, 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, which would ease our reliance on
supercomputers and increase our computational capacity to model even
bigger problems. That\'s right.

Bring it on.

https://tech.slashdot.org/story/20/10/30/1727201/ai-has-cracked-a-key-
mathematical-puzzle-for-understanding-our-world


--
Science teaches us to trust. - sw

Doesn\'t sound like a real big deal, and unlikely to work as well as they say. Just more over-hyped nerdology.
https://www.technologyreview.com/2020/10/30/1011435/ai-fourier-neural-network-cracks-navier-stokes-and-partial-differential-equations/
 

Welcome to EDABoard.com

Sponsor

Back
Top