A physics-guided deep learning framework for county-level maize yield estimation in arid irrigated regions

Accurate county-level maize yield estimation in arid irrigated regions remains challenging because yield–environment relationships are highly non-stationary and irrigation can decouple crop water status from meteorological forcing. To address this challenge, a hybrid Physics-Guided Deep Learning (PGDL) framework is proposed that couples a differentiable biomass-production pathway with a data-driven residual-correction module, embedding agronomic process knowledge directly into the learning architecture to improve both accuracy and interpretability. Xinjiang (Northwest China, 2000–2023) was selected as a representative case study for its long-term county-level yield records and pronounced spatial heterogeneity in irrigation practice. The model inputs combined daily-scale meteorological drivers from ERA5-Land (temperature, precipitation, Vapor Pressure Deficit, Photosynthetically Active Radiation), MODIS-derived canopy indicators (NDVI, EVI, LAI, FPAR, phenology from MCD12Q2), a thermal-based Mulching Index from MOD11A2, static soil properties from OpenLandMap, and NASADEM topography; annual maize masks were derived from Landsat 5/7/8/9 Collection 2 imagery. PGDL was benchmarked against Multiple Linear Regression, Random Forest, eXtreme Gradient Boosting, and a CNN–LSTM network, representing progressively stronger baselines from linear through tree-based to deep-sequence models. Under a strict temporal hold-out (2022–2023), PGDL achieved the best generalization (R² = 0.74, RMSE = 1091.9 kg ha⁻¹, MAE = 816.6 kg ha⁻¹), reducing RMSE by 11.8–29.5 % and MAE by 10.7–28.2 % relative to all baselines. An irrigation-proxy ablation indicated that explicit irrigation information contributed mainly to the physics-only pathway (ΔR² up to 0.031 in 2022), whereas its marginal value in the full model was negligible (|ΔR²| ≤ 0.001). Learned physiological parameters exhibited coherent spatial structure, and Geographically and Temporally Weighted Regression revealed systematic spatial differences in the relative contributions of the physical and residual components, delineating physics-dominant versus data-driven-dominant zones. These results demonstrate that the proposed framework improves accuracy, cross-year robustness, and interpretability of county-scale yield mapping in management-intensive arid systems.