Learning Structured Population Models from Data with WSINDy

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.