Opportunity

Lab Visits

For those interested in visiting our laboratory, please feel free to contact Yuzuru Kato (katoyuzu(at)fun.ac.jp).

Laboratory Overview

[Nonlinear Systems Laboratory]
We study physical systems that exhibit nonlinear phenomena by using mathematical sciences and data analysis. We deal with questions such as: How can we model a system? What kinds of dynamical behaviors does it exhibit? What information can we extract from the data it generates? And what kinds of controllers can we design for it?

Complex systems found across physics, biology, chemistry, engineering, and economics are, in fact, almost all nonlinear systems. In our lab, students are encouraged to freely design their own research themes based on complex phenomena that interest them, and to uncover the underlying structures of these systems through the power of mathematics and computer.

Yuzuru Kato works across nonlinear phenomena in a wide range of scales, from microscopic systems described by quantum mechanics to macroscopic systems described by classical mechanics. He is particularly interested in synchronization phenomena observed in various areas, such as atomic ensembles, neurons, pedestrian steps, and chemical reactions. Accordingly, His research focuses mainly on topics in physics, such as quantum mechanics and nonlinear dynamics, as well as in mathematical engineering, including control theory and machine learning.

＜Nonlinear Systems: Control and Optimization＞

We design control methods to manipulate nonlinear systems.For example, when the target system is a nonlinear oscillator, it is possible to control the phase distribution of a population of oscillators so that it converges to a desired distribution. Such approaches can contribute to advances in therapies that exploit synchronization phenomena, such as deep brain stimulation.

＜Data Analysis of Nonlinear Systems＞

We aim to uncover the mathematical structures underlying nonlinear dynamics from time-series data using data analysis methods such as machine learning. By employing tools like neural networks (e.g., autoencoders) and time-series analysis techniques (e.g., dynamic mode decomposition), we investigate the dynamic structures of complex systems. These approaches are useful, for instance, in extracting oscillatory patterns of vortices generated by jet engines or fluid flows, as well as biological rhythms in living systems.

＜Nonlinear dynamics in quantum systems＞

With the recent advances in nanotechnology, nonlinear phenomena based on quantum mechanics have attracted increasing attention. Microscopic systems described by quantum mechanics can exhibit behaviors that are completely different from those of macroscopic systems governed by classical mechanics. In this research, we aim to discover novel nonlinear phenomena in quantum systems.

So far, our work has included analyzing synchronization phenomena in quantum systems and proposing an activator-inhibitor systems model for Turing instabilities in quantum systems. In the future, these studies are expected to contribute to the design of quantum devices and the advancement of quantum information processing.

＜Quantum Machine Learning Using Quantum Computers＞

Machine learning that is carried out using quantum information processing, such as replacing neural networks with quantum computers, is called quantum machine learning. In this research, we aim to develop quantum machine learning methods that can perform tasks such as estimating dynamics of quantum systems, using real quantum computers and their simulators.

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