A Study on Methods for Extracting Deterministic Governing Equations from Complex Time Series

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K12111
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 61030:Intelligent informatics-related
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Hino Hideitsu 統計数理研究所, モデリング研究系, 教授 (10580079)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 作用素論的データ解析 / 動的モード分解 / ベイズ推論

Outline of Final Research Achievements

We reformulated the Bayesian model of dynamical mode decomposition, which is widely used mainly in the field of numerical fluid dynamics. We also developed a methodology for characterizing the nonlinear dynamical system behind a multidimensional nonlinear time series by assuming a nonlinear dynamical system. As a representative existing approach, a methodology called Koopman mode decomposition (KMD) has been actively studied. Based on the idea of linking the low-dimensional feature space extracted by Gaussian process latent modeling and the low-dimensional nonlinear dynamical system extracted by Koopman mode decomposition, we naturally formulated the existing deterministic KMD as a Bayesian framework.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

観測データから系の支配方程式を抽出することは，多くの科学・工学領域において中心的な課題である．しかし，例えば生物学，神経科学のように，明確な物理現象・化学プロセスに基づくモデルが明らかにされていない分野も多い．本研究では，潜在構造が明らかでない複雑時系列データから，系の時間遷移を記述する力学系を同定する方法論の開発した．本研究の成果は基礎方程式が十分に確立していない分野の大幅な発展に結びつく可能性を有しており，また，開発する数理的手法そのものが観測時系列の背後の潜在構造を解析する有用な方法論となりうる．