WEAK FORM LEARNING FOR MEAN-FIELD PARTIAL DIFFERENTIAL EQUATIONS: AN APPLICATION TO INSECT MOVEMENT.

Area of Science:

• Ecology
• Mathematical Biology
• Computational Science

Background:

• Insect movement is often stochastic due to environmental factors and predation.
• Understanding insect dispersal is crucial for predicting pest outbreaks and improving management.
• Existing data-driven models can struggle with sparse datasets.

Purpose of the Study:

• To develop and apply advanced equation learning techniques for modeling insect movement.
• To create effective models for lepidopteran larval population dynamics using sparse data.
• To forecast pest outbreaks more accurately by understanding dispersal patterns.

Main Methods:

• Utilizing weak-form equation learning techniques combined with kernel density estimation.
• Applying the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm.
• Analyzing sparse positional data from fall armyworms (Spodoptera frugiperda) in simulated agricultural settings.

Main Results:

• Successfully learned effective models for insect population movement from highly sparse data.
• Demonstrated the utility of weak-form equation learning for ecological modeling.
• Validated the approach using experimental data under varied conditions (plant resources, infection status).

Conclusions:

• Weak-form equation learning is a powerful tool for modeling complex biological systems with limited data.
• The developed models can enhance the prediction of insect pest dispersal and outbreaks.
• This methodology offers a pathway to improved pest management strategies in agriculture and silviculture.