Nonlinear System Analysis and its Applications to Machine Learning
I have studied mainly chaotic phenomena.
Chaotic phenomena are observed in a wide range of nonlinear systems such as atmospheric phenomena, chemical reactions, electronic circuits, etc.
Although they are based on deterministic dynamics, they seem to be disordered at first glance.
That is, it is difficult to predict their behavior over a long time because of the sensitivity to initial conditions to be described as the butterfly effect.
However, they show beautifully ordered behavior statistically and probabilistically.
Then, by dealing with chaotic phenomena probabilistically with the Ergodic theorem, I have approached analytically the chaotic phenomena which are often dealt with by numerical simulations.
In particular, if we prove the ergodicity of target systems, we can analyze various observables using the ergodic invariant density and it is a big advantage.
Specifically, I have derived the critical exponents of the Lyapunov exponents and proven the relaxation of the density functions to the equilibrium distribution by showing the ergodic properties.
Historically, in addition to studies on the chaotic phenomena themselves, studies that try to solve various problems using chaos have been actively carried out. In my future research, I would like to proceed with the same research as before, and at the same time, based on my knowledge so far, I would like to tackle problems such as information processing.
March 2020 Ph.D., Kyoto University (Informatics)
April 2020 Specially Appointed Assistant Professor, Graduate School of Information Science and Technology, Osaka University
- E-mail ： okubo@ist.
- Tel ： S7834
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