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Learning Both Dynamic-Shared and Dynamic-Specific Patterns for Chaotic Time-Series Prediction.

Shoubo Feng, Min Han, Jiadong Zhang

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    This study introduces a novel multitask learning (MTL) model for predicting chaotic time series. The model effectively identifies shared patterns in complex dynamical systems, improving prediction accuracy.

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    Area of Science:

    • Dynamical Systems and Chaos Theory
    • Machine Learning
    • Time Series Analysis

    Background:

    • Multivariate time series from dynamical systems exhibit deterministic relationships, making individual analysis inefficient.
    • Multitask learning (MTL) leverages shared features across related tasks to improve learning efficiency and discover structural relationships.

    Purpose of the Study:

    • To propose a novel MTL model for multivariate chaotic time-series prediction.
    • To effectively learn both dynamic-shared and dynamic-specific patterns within complex systems.
    • To disentangle intricate relationships and identify common evolutionary trends in multivariate chaotic dynamical systems.

    Main Methods:

    • A specialized network architecture is designed for dynamic analysis of multiple time series.
    • The proposed model utilizes inductive bias to capture latent shared features.
    • An efficient Crank-Nicolson-like curvilinear update algorithm based on ADMM is developed for a nonconvex nonsmooth Stiefel optimization problem.

    Main Results:

    • The model successfully disentangles complex relationships among multivariate chaotic time series.
    • It effectively derives the common evolutionary trend of the multivariate chaotic dynamical system.
    • Simulation results confirm the model's effectiveness in discovering dynamic-shared patterns and enhancing prediction performance.

    Conclusions:

    • The proposed MTL model offers an effective approach for analyzing and predicting multivariate chaotic time series.
    • The network structure and optimization algorithm contribute to improved understanding of dynamical system dynamics.
    • This work advances the application of MTL in complex time series prediction tasks.