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    Area of Science:

    • Complex Systems and Data Science
    • Time Series Analysis and Dynamical Systems

    Background:

    • Missing data in time series is a common challenge across diverse fields like medicine and climatology, hindering data mining and analysis.
    • Existing methods often focus on interpolation or task-specific adaptations, leaving a gap for generalizable irregular time series recovery.

    Purpose of the Study:

    • To develop an iterative learning method based on reservoir computing (RC) for systematically recovering missing data in irregular time series.
    • To formulate the data recovery as a fixed-point iterative learning problem solvable with an RC network (RCN).

    Main Methods:

    • Developed an iterative learning procedure using an RC network (RCN) to address missing data in irregular time series.
    • Formulated the problem as a fixed-point iterative learning task.
    • Derived conditions for reservoir parameters to ensure convergence of the iterative procedure.

    Main Results:

    • Demonstrated successful systematic recovery of missing data in irregular time series when sufficient samples are available for RCN training.
    • Validated the approach on chaotic Rössler and Kuramoto-Sivashinsky (KS) systems, showcasing its efficacy.
    • Showcased the method's applicability by incorporating it into an irregular medical data classification task.

    Conclusions:

    • The proposed iterative RCN approach offers a robust and systematic solution for recovering missing data in irregular time series from dynamical systems.
    • The method shows promise for practical applications, including complex system analysis and medical data processing.