Learning structured population models from data with WSINDy

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.