「運動論方程式,流体力学とその周辺」(第4回)

各位

京都大学 航空宇宙工学専攻 高田 滋

下記のとおり日本航空宇宙学会関西支部分科会による講演会を開催しますのでご案内いたします.

http://www.mfd.kuaero.kyoto-u.ac.jp/?cat=16

– 記 –
日時: 2019年1月18日(金) 16:30-17:30
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室)

題目:
Data-driven modelling of dynamical system based on delay-embedding
講演者:
Prof. Naoto Nakano (Center for Innovative Research and Education in Data
Science, Institute for Liberal Arts and Sciences & Graduate School of
Science, Kyoto University, Japan)
中野 直人 講師 (京都大学 国際高等教育院附属データ科学イノベーション教育研究センターおよび理学研究科)
要旨:
Delay embedding is well-known for non-linear time-series analysis, and it
is used in several research fields such as physics, informatics,
neuroscience and so forth. The celebrated theorem of Takens (1981) ensures
validity of the delay embedding analysis: embedded data preserves
topological properties which the original dynamics possesses. This method
is easy to implement for time-series analysis, however, resultant embedded
dataset may easily vary with the delay width and the delay dimension,
namely, “the way of embedding”. In a practical sense, this sensitivity may
sometimes interfere with users’interpretation of embedded objects. In this
study, to derive an appropriate embedding Ansatz, we investigate the
mathematical structure of delay-embedding from a view point of linear
operator theory. In this talk, we will briefly overview its framework, and
we will show some numerical results of time-series analysis by the present
method. For example, prediction, attractor reconstruction, causality
detection and control problems.