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    This study introduces a novel Scientific Machine Learning method to efficiently identify key population dynamics features from data. The approach simplifies complex ecological modeling by selecting essential model components and learning population boundaries.

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    Area of Science:

    • Ecology
    • Computational Biology
    • Mathematical Biology

    Background:

    • Identifying key features like fecundity and mortality in population dynamics is challenging, especially with heterogeneous populations.
    • Existing methods for modeling structured populations can be computationally intensive and complex.

    Purpose of the Study:

    • To propose a Weak form Scientific Machine Learning (WSINDy) based method for selecting model ingredients for structured populations.
    • To extend WSINDy to handle heterogeneous dynamics and learn boundary processes directly from data.
    • To introduce a cross-validation technique for refining the learned boundary process.

    Main Methods:

    • Utilizing extensions of the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) method.
    • Applying the method to noisy time-series histogram data.
    • Incorporating learning of heterogeneous dynamics and boundary processes.
    • Employing a cross-validation approach for parameter tuning.

    Main Results:

    • Demonstrated the method's effectiveness on various structured population models (age, size-structured).
    • Successfully selected appropriate model ingredients from a library of functions.
    • Showcased the ability to learn heterogeneous dynamics and boundary processes from data.
    • Examined the advantages and limitations, focusing on term distinguishability.

    Conclusions:

    • The proposed WSINDy-based method offers an efficient approach to identifying essential components in structured population dynamics.
    • The method effectively handles noisy data, heterogeneous dynamics, and boundary processes.
    • Further analysis is needed to fully understand the distinguishability of library terms under various conditions.