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    This study integrates machine learning with the generalized Langevin equation (GLE) to model complex systems. The new approach overcomes data limitations, offering accurate predictions for observable dynamics in diverse fields.

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    Area of Science:

    • Physics
    • Statistical Mechanics
    • Machine Learning

    Background:

    • The generalized Langevin equation (GLE) models complex physical systems but requires inaccessible historical data.
    • Challenges include dependence on complete observable histories and microscopic details.

    Purpose of the Study:

    • To overcome the limitations of the generalized Langevin equation (GLE) using machine learning.
    • To develop a computational tool for describing noisy complex systems.

    Main Methods:

    • Coupling a multilayer perceptron (MLP) with the formal structure of GLE.
    • Calibrating the MLP using empirical data.

    Main Results:

    • The combined MLP-GLE framework accurately describes observable dynamics.
    • Successful application demonstrated in diverse fields like physics, climatology, and finance.

    Conclusions:

    • This novel framework provides a powerful computational tool for analyzing complex systems.
    • It offers a new perspective on non-equilibrium processes and stochastic modeling.