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Rainey Lyons1, Vanja Dukic1, David M Bortz1

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado, United States of America.

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|December 8, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a novel Scientific Machine Learning method to efficiently identify key factors driving population changes from data. The approach simplifies modeling complex population dynamics, including heterogeneous populations.

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Area of Science:

  • Population Dynamics
  • Scientific Machine Learning
  • Computational Biology

Background:

  • Population dynamics are influenced by individual characteristics like age and size.
  • Identifying key factors (e.g., fecundity, mortality) in population models is computationally challenging, especially for heterogeneous populations.
  • Existing methods struggle with noisy data and learning complex dynamics.

Purpose of the Study:

  • To develop a Weak form Scientific Machine Learning (WSINDy) method for selecting model components for structured populations.
  • To extend WSINDy for learning heterogeneous population dynamics and boundary processes directly from noisy time-series histogram data.
  • To incorporate cross-validation for fine-tuning hyperparameters of learned boundary processes.

Main Methods:

  • Proposed an extension of the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) method.
  • Applied the method to noisy time-series histogram data to identify model ingredients.
  • Incorporated a cross-validation technique for hyperparameter tuning.

    • Main Results:

    • Successfully demonstrated the method's performance on standard age and size-structured population models.
    • Showcased the ability to learn heterogeneous dynamics and boundary processes (e.g., birth) from data.
    • Examined the advantages and limitations, focusing on the distinguishability of library terms.

    Conclusions:

    • The proposed WSINDy extension offers an efficient approach to model selection in population dynamics.
    • The method effectively handles noisy data and learns complex, heterogeneous population dynamics.
    • This approach advances the ability to model structured populations by directly inferring model components and boundary processes.