Machine-learning-assisted construction of appropriate rotating frame - Paper slide summary

Aug 2, 2026

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Machine-learning-assisted methods are proposed to derive analytical frameworks for periodically driven quantum systems by constructing an appropriate rotating frame. The work uses recurrent neural networks to generate the Floquet-Magnus expansion directly from a time-periodic Hamiltonian input. It then extracts the appropriate rotating frame in the driven system and argues the approach can extend to other theoretical frameworks, enabling scale-separation properties that are difficult to identify manually.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Introduction

Motivation: theoretical analysis with machine learning

Rotating frame and scale separation in periodically driven systems

Proposed method and scope

Concrete procedure to construct the rotating frame

Machine-learning-assisted construction of appropriate rotating frame arXiv :2211 . 15269v4 [ cond-mat .dis-nn] 11 Apr 2023 Yoshihiro Michishita 1, 􀀃 1 RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan (Dated: April 12, 2023) 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 􀀌nd the analytical method are poorly studied. In this letter, we propose methods to use machine learning to 􀀌nd 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 􀀌nding other theoretical frameworks in other systems. Introduction. { Machine learning with neural networks (NN) is now becoming a powerful tool for various tasks, such as natural language processing[1], image recognition[2{4], and winning the game[5] . As for the issues of physics, machine learning can be used for phase detection[6{11], solving the equilibrium state[12{14] or steady state[15], materials informatics[16{19] and noise reduction of the experimental measurement results[20] . While experimental detection and numerical calculation with the aid of machine learning are now making great progress, one might have a natural question: Can we develop theoretical analysis methods with the aid of machine learning? Before tackling this question, let us consider how we ourselves have developed the theoretical analysis methods so far. One of the central techniques is scale separation, which leads to the reduction and the perturbation theory. A typical example is a derivation of the Langevin equation, in which, by utilizing the time-scale separation between the microparticles' motion and the Brownian particles' motion, we perform the reduction of the degrees of freedom of the microparticles and get the stochastic equation of motion.[21] Other examples are the dimensional reduction of nonlinear dynamical systems[22], the derivation of the Heisenberg model from the Hubbard model in half-􀀌lling and large interaction limit[23], therenormalization group methods[24], and so on. However, in general, it is a non-trivial problem to 􀀌nd and separate the fast process and the slow process of the system, and we have to perform an appropriate unitary transformation or projection and get the frame in which the scale separation is apparent. [25{32] In periodically-driven systems, we introduce an appropriate rotating frame (RF) associated with the timeperiodic unitary transformation and separate fast and slow modes. It is known that, under high-frequency driving where the frequency is larger enough than the energy scale of the system, the system stays the Floquet prethermalized before going to the in􀀌nite temperature state[33{35], and we can engineer the desired state in the Floquet prethermalized state.[36{43] In the highfrequency regime, we can construct an appropriate RF with high-frequency expansion.[44] In such an appropriate RF, the e􀀋ective static Hamiltonian describes the Floquet prethermalized state, and the dressed driving term describes the heating rate.[44, 45] Therefore, 􀀌nding an appropriate unitary transformation or projection and a scale separation is highly bene􀀌cial, while it is usually di􀀎cult. In this letter, we propose a method to search for the appropriate frame with desirable properties using machine learning techniques. Our method has the advantage that it is enough to set the desirable properties asa loss function and, thus, should be ver

FAQs

What problem does the paper address regarding machine learning in physics?

It targets the challenge of using machine learning to find analytical methods rather than only numerical computation or experimental assistance.

How does the method derive the Floquet-Magnus expansion?

It feeds the time-periodic Hamiltonian into recurrent neural networks, which output the Floquet-Magnus expansion.

What is the role of the appropriate rotating frame in periodically driven systems?

The rotating frame enables a separation of fast and slow modes, yielding an effective static Hamiltonian for the Floquet prethermalized state and describing heating through dressed driving terms.

Aug 2, 2026

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