Mathematics and physics use simplified models to describe quantum phenomena. But even in this case, hundreds, thousands, and even millions of equations have to be dealt with to describe the interaction processes of a finite number of particles at the level of quantum mechanics.

For example, to visualize the pattern of interaction of two electrons in a crystal lattice node, 100,000 equations must be solved, one for each pixel of the visualization. This requires enormous computing resources. But AI promises to cope with such a task without unnecessary costs.

A new machine learning model

An international group of Italian and American physicists and mathematicians has managed to create such a machine learning model that reduces the solution of the problem to just four equations per pixel. Moreover, without loss of accuracy. True, training the AI ​​took two weeks of intense calculations, but the result paid off. Also, the proposed model can be used to solve other problems with the related mathematical device – the renormalization group method, which will expand the scope of the proposed tool to elementary particle physics (cosmology) and neuroscience.

In fact, this machine is capable of detecting hidden patterns. When we saw the result, we realized that it was more than we expected. We did indeed manage to capture the physics involved,
– said Domenico Di Sante, lead author of the study.

Usually, the renormalization group method works with many parameters and acts as a support for scaling operations. The researchers built an AI model that first creates links in a full-size renormalization group without simplification, and then modifies these links in a way that reduces all calculations to a small set of equations while maintaining a similar result.

The final result is preserved, but the paths to it differ by many orders of magnitude of the computational power required. Interestingly, scientists do not yet understand how AI calculates optimization paths, but they plan to solve this in future research.