AI-Augmented Mathematical Modeling of Spray Deposition and Environmental Impact in UAV-Based Precision Agriculture

The accurate modeling of spray deposition dynamics is essential for assessing the efficiency and environmental consequences of UAV-based precision agriculture. Traditional fluid mechanics and physical dispersion models, while valuable, often struggle to capture the complexity of real-world spraying conditions influenced by canopy heterogeneity, wind variation, and nozzle type. This study proposes an AI-augmented mathematical framework that integrates partial differential equation (PDE)-based spray dispersion models with statistical learning methods to improve prediction accuracy. Random forests and gradient boosting algorithms are employed to calibrate and refine predictions from field-collected UAV spray data, while principal component analysis and multivariate regression identify the dominant factors affecting deposition efficiency, including droplet size, nozzle angle, wind speed, and canopy density. Experimental validation in orchard conditions demonstrates that the hybrid PDE–AI model achieves superior accuracy over traditional physics-only approaches, thus reducing the prediction error by more than 20%. Beyond operational optimization, the framework also quantifies reductions in pesticide use, water footprint, and CO₂ emissions, thereby linking mathematical modeling with sustainability objectives. The results confirm that combining mathematical analysis with AI not only improves predictive capability but also supports decision-making for environmentally responsible precision spraying practices. This research highlights the potential of hybrid mathematical–statistical approaches to advance sustainable agriculture.