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Agricultural robotics-enabled crop health monitoring faces critical trade-offs: standalone on-device models sacrifice accuracy for real-time responsiveness, while cloud-dependent approaches suffer from high latency and communication overhead. Additionally, data-driven models often lack biophysical plausibility, leading to unreliable predictions for agronomic decision-making under resource constraints. We propose a hybrid LSTM-edge correction architecture that hierarchically integrates lightweight Long Short-Term Memory (LSTM) networks on field robots with physics-informed neural networks (PINNs) at the edge. On-device LSTMs process localized sensor data (soil moisture, spectral reflectance) to generate initial crop stress probability estimates with minimal latency. Edge-based PINNs refine these predictions by embedding biophysical dynamics—modeled via coupled partial differential equations (PDEs) governing the soil-plant-atmosphere continuum (SPAC)—to ensure agronomic validity, mitigate sensor noise, and account for spatial variability. The framework is deployed on NVIDIA Jetson Nano (local inference) and AMD EPYC servers (edge processing), seamlessly integrating with existing farming infrastructures to replace rule-based thresholds with adaptive, physics-grounded control commands. A Fourier Neural Operator (FNO) optimizes the edge PINN’s computational efficiency for high-dimensional PDE solving. Experimental evaluations on two real-world datasets (soybean and citrus) demonstrate that the hybrid approach improves prediction accuracy by 18% compared to standalone LSTMs (F1-score: 0.89±0.02 for soybean, 0.83±0.03 for citrus) while maintaining real-time performance (end-to-end latency: 210 ms, energy consumption: 5.1 J/prediction). Field deployment on a 50-hectare soybean farm yields tangible agronomic benefits: 22% reduction in irrigation water usage, 18% fewer pesticide applications, and 95% system uptime under field conditions. The framework exhibits robust performance against sensor noise (≥80% accuracy at 30% noise-to-signal ratio) and outperforms cloud-based PINNs (72.8% lower energy consumption) and threshold-based methods (28–33% higher F1-score). This work advances distributed agricultural robotics by bridging data-driven machine learning and domain-specific physics, delivering a scalable, interpretable, and resource-efficient solution for precision agriculture. The hierarchical prediction-correction pipeline balances real-time responsiveness with biological plausibility, making it suitable for resource-constrained field robots. By integrating legacy sensors and adaptive actuation control, the architecture offers a practical pathway to upgrade existing farming systems, enabling data-informed interventions while reducing environmental impact.