PDEs cracked by Artificial Intelligence at Cal Tech

In summary, researchers have developed an AI system that can solve complex partial differential equations, such as the Navier-Stokes equation for fluid dynamics, by using a Fourier neural network. This method greatly simplifies the neural network's job and is capable of solving entire families of PDEs without retraining. It is also 1000 times faster than traditional mathematical formulas. However, some argue that this is simply function approximation rather than true artificial intelligence.
  • #1
Tom.G
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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
 
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  • #2
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.
 
  • #3
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?
 
  • #4
IMO it's not really "AI". It is function approximation, there is nothing intelligent about it. The natural intelligence of the researchers is real.
 
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  • #5
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.
 

1. What are PDEs and how are they used in science?

PDEs, or partial differential equations, are mathematical equations that involve multiple variables and their partial derivatives. They are used to model and understand complex physical phenomena, such as heat transfer, fluid dynamics, and quantum mechanics.

2. How is Artificial Intelligence used to solve PDEs at Cal Tech?

At Cal Tech, researchers have developed AI algorithms that can efficiently and accurately solve PDEs. These algorithms use machine learning techniques to learn from data and make predictions, allowing them to handle the complex and nonlinear nature of PDEs.

3. What are the benefits of using AI to solve PDEs?

Using AI to solve PDEs can lead to faster and more accurate solutions compared to traditional numerical methods. Additionally, it can handle more complex and high-dimensional problems that would be difficult for traditional methods to solve.

4. What are some potential applications of this research?

This research has potential applications in various fields, such as engineering, physics, and finance. It can be used to optimize designs, simulate physical systems, and make predictions in financial markets.

5. What are the future implications of PDEs being solved by AI?

The use of AI to solve PDEs has the potential to revolutionize the way we approach and solve complex problems in science and engineering. It could lead to more efficient and accurate solutions, as well as new insights and discoveries in various fields.

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