Lightweight U-Net Architectures for Mathematics-Informed AI in Variable-Rate Spraying

Variable-rate spraying (VRS) is an essential component of precision agriculture, enabling targeted agrochemical application according to spatial and canopy variability. This work introduces a mathematics-informed deep learning framework that integrates lightweight U-Net architectures, such as U-Net Mini, with optimization-based spray allocation strategies for UAV spraying systems. The encoder–decoder design of U-Net, grounded in variational principles of image analysis, is employed to segment UAV-acquired imagery into canopy and non-canopy regions. From these segmentation masks, geometric measures of canopy area and density are computed to characterize crop heterogeneity. A constrained optimization model is then applied to allocate spray volumes proportionally to canopy demand, ensuring efficiency under limited resource budgets. To enable practical deployment on UAV platforms, parameter-reduced variants of U-Net are explored, demonstrating significant reductions in computational cost while maintaining high segmentation accuracy (IoU > 0.85). When combined with optimization-based variable-rate control, the proposed system reduces chemical usage and spray drift compared to fixed-rate application. The study highlights how mathematical concepts—variational modeling, optimization theory, and geometric analysis—can be embedded within AI architectures to provide efficient, interpretable, and sustainable solutions for UAV-based precision spraying. This fusion of mathematical modeling with lightweight deep learning offers a promising pathway for scalable field applications and environmentally responsible agriculture.