Model Reduction for High-dimensional Nonlinear Chaotic Dynamical Systems Based on Kernel Multivariate Analysis

2011 Fiscal Year Final Research Report

• Project/Area Number: 22740258
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kagoshima University
• Principal Investigator: SUETANI Hiromichi 鹿児島大学, 大学院・理工学研究科, 准教授 (40507167)
• Project Period (FY): 2010 – 2011
• Keywords: 非平衡 / 非線形物理学 / 時系列解析 / カーネル法 / 多様体学習 / カオス / データ同化 / 水滴落下

Research Abstract

We improved ISOMAP, which is a representative manifold learning method, by preventing mistakes in estimating geodesics between points in a manifold using RANSAC. We applied the proposed approach to the numerical simulation data generated from a mass-spring model for dripping faucet in order to demonstrate the usefulness. Furthermore, we tried to analyze real data of the dripping faucet experiment and obtained promising results.

Research Products

• [Journal Article] A RANSAC-Based ISOMAP for Filiform Manifolds in Nonlinear Dynamical Systems-An Application to Chaos in a Dripping Faucet (2011)
  • Author(s): Hiromichi Suetani and Shotaro Akaho
  • Journal Title: Lecture Notes in Computer Science Volume: 6792巻 Pages: 277-284
  • DOI: DOI:10.1007/978-3-642-21738-8_36
  • Peer Reviewed
• [Presentation] A Manifold Learning Approach for Assimilating Chaotic Dynamical Systems (2012)
  • Author(s): Hiromichi Suetani
  • Organizer: Dynamics days 2012
  • Place of Presentation: Sheraton Inner Harbor Hotel/Baltimore Maryland America
  • Year and Date: 2012-01-09
• [Presentation] 水滴落下に対するバネ-質点モデルの修正と多様体学習による解析 (2011)
  • Author(s): 末谷大道, 黒岩宏紀, 秦浩起
  • Organizer: 2011年物理学会秋季大会
  • Place of Presentation: 富山大学
  • Year and Date: 2011-09-22
• [Presentation] Manifold Learning Approach for Reconstructing Internal States from Partially Observed Data : An Application to Assimilating Series of Events Generated from Nonlinear Dynamical Systems (2011)
  • Author(s): Hiromichi Suetani, Aiko Ideta, Shotaro Akaho, D. Engster, and U. Parlitz
  • Organizer: 5th International Scientific Conference on Physics and Control
  • Place of Presentation: Physcon 2011(University of Leon/Spain)
  • Year and Date: 2011-09-08
• [Presentation] カーネル法による水滴カオスの解析 (2011)
  • Author(s): 末谷大道, 黒岩宏紀, 秦浩起
  • Organizer: 日本物理学会第66回年次大会
  • Place of Presentation: 新潟大学
  • Year and Date: 2011-03-28