Sensitivity analysis of chaotic dynamical systems using a physics-constrained data-driven approach

2022 ◽  
Vol 34 (1) ◽  
pp. 014101
Author(s):  
Hamid R. Karbasian ◽  
Brian C. Vermeire
Keyword(s):  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Data Driven ◽  
Chaotic Dynamical Systems ◽  
Data Driven Approach

Data-Driven Detection and Classification of Regimes in Chaotic Systems Via Hidden Markov Modeling

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Chandrachur Bhattacharya ◽  
Asok Ray
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Hidden Markov ◽  
Urban Traffic ◽  
Data Driven ◽  
Bench Mark ◽  
Lorenz Attractor ◽  
Markov Modeling ◽  
Chaotic Dynamical Systems ◽  
Hidden Markov Modeling

Abstract Chaotic dynamical systems are essentially nonlinear and are highly sensitive to variations in initial conditions and process parameters. Chaos may appear both in natural (e.g., heartbeat rhythms and weather fluctuations) and human-engineered (e.g., thermo-fluid, urban traffic, and stock market) systems. For prediction and control of such systems, it is often necessary to be able to distinguish between non-chaotic and chaotic behavior; several methods exist to detect the presence (or absence) of chaos, specially in noisy signals. A dynamical system may exhibit multiple chaotic regimes, and apparently, there exist no methods, reported in open literature, to classify these regimes individually. This paper demonstrates an application of standard hidden Markov modeling (HMM), which is a commonly used supervised method, as a technique to classify multiple regimes from a time series of dynamical systems, where classified regimes could be chaotic or non-chaotic. The proposed HMM-based method of regime classification has been tested using numerical data obtained from several well-known chaotic dynamical systems (e.g., Hénon, forced Duffing, Rössler, and Lorenz attractor). It is apparently well-suited to serve as a bench mark for the development of alternative data-driven methods to enhance the performance (e.g., accuracy and computational speed) of regime classification in chaotic dynamical systems.

A data-driven approach to model calibration for nonlinear dynamical systems

2019 ◽  
Vol 125 (24) ◽  
pp. 244901 ◽  
Author(s):  
C. M. Greve ◽  
K. Hara ◽  
R. S. Martin ◽  
D. Q. Eckhardt ◽  
J. W. Koo
Keyword(s):  
Dynamical Systems ◽  
Model Calibration ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Nonlinear Dynamical ◽  
Data Driven Approach
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