Machine-learning-assisted construction of appropriate rotating frame

TL;DR

This paper demonstrates how neural networks can be used to derive analytical methods in physics, such as the Floquet-Magnus expansion and appropriate rotating frames, by learning from time-periodic Hamiltonians.

Contribution

It introduces a novel approach using machine learning to discover analytical frameworks in physics, which has been less explored compared to numerical or experimental applications.

Findings

Neural networks can derive the Floquet-Magnus expansion from time-periodic Hamiltonians.

The method can identify appropriate rotating frames in driven quantum systems.

Potential applicability to other theoretical frameworks in physics.

Abstract

Machine learning with neural networks is now becoming a more and more powerful tool for various tasks, such as natural language processing, image recognition, winning the game, and even for the issues of physics. Although there are many studies on the application of machine learning to numerical calculation and the assistance of experimental detection, the methods of applying machine learning to find the analytical method are poorly studied. In this letter, we propose methods to use machine learning to find the analytical methods. We demonstrate that the recurrent neural networks can ``derive'' the Floquet-Magnus expansion just by inputting the time-periodic Hamiltonian to the neural networks, and derive the appropriate rotating frame in the periodically-driven system. We also argue that this method is also applicable to finding other theoretical frameworks in other systems.