TY - JOUR
T1 - Chaotic behavior learning via information tracking
AU - Ren, Jinfu
AU - Liu, Yang
AU - Liu, Jiming
N1 - This work was supported in part by the National Key Research and Development Program of China from the Ministry of Science and Technology of China under the Projects 2021ZD0112501 and 2021ZD0112502 , in part by the National Natural Science Foundation of China/RGC Joint Research Scheme under the Project N_HKBU222/22 , and in part by the General Research Fund from the Research Grant Council of Hong Kong SAR under Projects RGC/HKBU12201619 and RGC/HKBU12203122.
Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/10
Y1 - 2023/10
N2 - Chaotic time series are often encountered in real-world applications, where modeling and understanding such time series present a significant challenge. Existing simulation-based methods for characterizing chaotic behavior may be sensitive to the respective model settings, while data-driven methods cannot adapt well to irregularities and aperiodicity in chaotic time series during the prediction stage, leading to nonlinearly aggregated forecasting errors after a finite number of time steps. In our preliminary work (Ren et al., 2023), we introduced a data-driven method that incorporates the idea of information tracking to capture and adapt to the chaotic changes over time, and tested its effectiveness on a real-world task—decadal temperature prediction. While the practical usefulness of the method has been initially validated on one domain-specific application scenario, a set of open questions is yet to be answered: Is the concept of information tracking generalizable to model and solve a broad spectrum of learning tasks that involve chaotic behavior? If yes, what are the underlying principles and learning behaviors that make the general method work well? Moreover, how can we assess the efficacy of the method in different scenarios? This study constitutes a significant step forward by systematically investigating and addressing the questions mentioned above. Specifically, we first provide a rigorous definition of the formalism and computational mechanism of the general method, with all necessary variables, symbols, and formulations. More importantly, we theoretically characterize and understand the generalizability of the method by mathematically uncovering the fundamental principles and behavior of information tracking-based chaotic behavioral learning, as prescribed by two chaotic behavioral indexes, namely, the Lyapunov and the Hurst exponents. Further, we comprehensively demonstrate the generalizability and robustness of the method by empirically examining a variety of chaotic behavioral learning problems generated by three representative chaotic systems: The logistic map, the double pendulum, and the Lorenz system.
AB - Chaotic time series are often encountered in real-world applications, where modeling and understanding such time series present a significant challenge. Existing simulation-based methods for characterizing chaotic behavior may be sensitive to the respective model settings, while data-driven methods cannot adapt well to irregularities and aperiodicity in chaotic time series during the prediction stage, leading to nonlinearly aggregated forecasting errors after a finite number of time steps. In our preliminary work (Ren et al., 2023), we introduced a data-driven method that incorporates the idea of information tracking to capture and adapt to the chaotic changes over time, and tested its effectiveness on a real-world task—decadal temperature prediction. While the practical usefulness of the method has been initially validated on one domain-specific application scenario, a set of open questions is yet to be answered: Is the concept of information tracking generalizable to model and solve a broad spectrum of learning tasks that involve chaotic behavior? If yes, what are the underlying principles and learning behaviors that make the general method work well? Moreover, how can we assess the efficacy of the method in different scenarios? This study constitutes a significant step forward by systematically investigating and addressing the questions mentioned above. Specifically, we first provide a rigorous definition of the formalism and computational mechanism of the general method, with all necessary variables, symbols, and formulations. More importantly, we theoretically characterize and understand the generalizability of the method by mathematically uncovering the fundamental principles and behavior of information tracking-based chaotic behavioral learning, as prescribed by two chaotic behavioral indexes, namely, the Lyapunov and the Hurst exponents. Further, we comprehensively demonstrate the generalizability and robustness of the method by empirically examining a variety of chaotic behavioral learning problems generated by three representative chaotic systems: The logistic map, the double pendulum, and the Lorenz system.
KW - Chaotic behavior characterization
KW - Information tracking
KW - Machine learning
KW - The Hurst exponent
KW - The Lyapunov exponent
UR - http://www.scopus.com/inward/record.url?scp=85170421649&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2023.113927
DO - 10.1016/j.chaos.2023.113927
M3 - Journal article
AN - SCOPUS:85170421649
SN - 0960-0779
VL - 175, Part 1
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 113927
ER -