# How artificial intelligence was taught to solve diffusion

Unless you are a physicist or engineer, you have no particular reason to know about partial differential equations. And after years of graduate school studying mechanical engineering, I haven’t used them in real life since.

But such equations, (hereinafter for simplicity, we use the English abbreviation PDE), have their own magic. This is a category of mathematical equations that are really good at describing changes in space and time, and thus very convenient for describing physical phenomena in our universe. They can be used to model everything from planetary orbits to plate tectonics and air turbulence interfering with flight, which in turn allows us to do useful things, such as predicting seismic activity and designing safe aircraft.

The catch is that PDEs are notoriously difficult to solve. And here the meaning of the word “decision” is perhaps better illustrated. For example, you are trying to simulate air turbulence in order to test a new airplane design. There is a well-known PDE called the Navier-Stokes equation, which is used to describe the motion of any fluid. Solving the Navier-Stokes equation allows you to take a “snapshot” of the movement of air (wind conditions) at any time and simulate how it will continue to move or how it moved before.

These calculations are very complex and computationally expensive, so disciplines with a lot of PDEs often rely on supercomputers to perform mathematical calculations. This is why AI professionals take a special interest in these equations. If we could use deep learning to speed up the solution, it could be of great benefit in research and engineering.

Koltech researchers have implemented new method of deep learning to solve PDE, which is significantly more accurate than the deep learning methods previously developed. The method is also generalized enough to solve entire PDE families such as the Navier-Stokes equation for any type of fluid, without the need for new training. Finally, it is 1,000 times faster than traditional mathematical formulas, reducing reliance on supercomputers and increasing the computational power of problem modeling even further. And this is good. Give two!

## Hammertime

[прим. перев. — Подзаголовок — отсылка к «U Can’t Touch This» за авторством рэпера MC Hammer]

Before we dive into how the researchers did it, let’s first evaluate the results. The gif below shows an impressive demo. The first column shows two snapshots of fluid movement; the second column shows how the fluid actually continued to move; and the third column shows the neural network prediction. Basically it looks identical to the second one.

The article did a lot of twitter buzz and even rapper MC Hammer repost.