Weak Form Learning for Mean-Field Partial Differential Equations: an Application to Insect Movement
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2025
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| author | Minor, Seth Elderd, Bret D. Van Allen, Benjamin Bortz, David M. Dukic, Vanja |
| author_facet | Minor, Seth Elderd, Bret D. Van Allen, Benjamin Bortz, David M. Dukic, Vanja |
| contents | Insect species subject to infection, predation, and anisotropic environmental conditions may exhibit preferential movement patterns. Given the innate stochasticity of exogenous factors driving these patterns over short timescales, individual insect trajectories typically obey overdamped stochastic dynamics. In practice, data-driven modeling approaches designed to learn the underlying Fokker-Planck equations from observed insect distributions serve as ideal tools for understanding and predicting such behavior. Understanding dispersal dynamics of crop and silvicultural pests can lead to a better forecasting of outbreak intensity and location, which can result in better pest management. In this work, we extend weak-form equation learning techniques, coupled with kernel density estimation, to learn effective models for lepidopteran larval population movement from highly sparse experimental data. Galerkin methods such as the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm have recently proven useful for learning governing equations in several scientific contexts. We demonstrate the utility of the method on a sparse dataset of position measurements of fall armyworms (Spodoptera frugiperda) obtained in simulated agricultural conditions with varied plant resources and infection status. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_07786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Form Learning for Mean-Field Partial Differential Equations: an Application to Insect Movement Minor, Seth Elderd, Bret D. Van Allen, Benjamin Bortz, David M. Dukic, Vanja Machine Learning Dynamical Systems Populations and Evolution 60J70, 62FXX, 92-08 Insect species subject to infection, predation, and anisotropic environmental conditions may exhibit preferential movement patterns. Given the innate stochasticity of exogenous factors driving these patterns over short timescales, individual insect trajectories typically obey overdamped stochastic dynamics. In practice, data-driven modeling approaches designed to learn the underlying Fokker-Planck equations from observed insect distributions serve as ideal tools for understanding and predicting such behavior. Understanding dispersal dynamics of crop and silvicultural pests can lead to a better forecasting of outbreak intensity and location, which can result in better pest management. In this work, we extend weak-form equation learning techniques, coupled with kernel density estimation, to learn effective models for lepidopteran larval population movement from highly sparse experimental data. Galerkin methods such as the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm have recently proven useful for learning governing equations in several scientific contexts. We demonstrate the utility of the method on a sparse dataset of position measurements of fall armyworms (Spodoptera frugiperda) obtained in simulated agricultural conditions with varied plant resources and infection status. |
| title | Weak Form Learning for Mean-Field Partial Differential Equations: an Application to Insect Movement |
| topic | Machine Learning Dynamical Systems Populations and Evolution 60J70, 62FXX, 92-08 |
| url | https://arxiv.org/abs/2510.07786 |