分科会「運動論方程式，流体力学とその周辺」（第7回）

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）
講演：	Data-driven modelling of dynamical system based on delay-embedding
	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.