Physics-informed deep learning for robust maize leaf area index estimation using multi-source data

Maize is one of the most important staple crops worldwide. Accurate leaf area index (LAI) estimation is essential for precise maize management. However, most existing methods rely on common machine learning models, which often suffer from poor spatiotemporal generalization. To address these issues, this study proposes PhysLAINet, a physics-informed model for maize LAI estimation based on multi-source data fusion. The model takes bi-temporal spectral–textural features and phenological variables as input, adopting a dual branch structure. The physical branch is built on a dynamic leaf area density (LAD) model, while the phenological branch is based on an enhanced logistic model. The outputs of the two branches are fused using an adaptive weighting strategy. In addition, an uncertainty weighted loss is introduced to constrain multi-stage LAI predictions. PhysLAINet incorporates explicit physical constraints, which helps reduce saturation effects and improves sensitivity to abnormal crop growth. Experimental results show that PhysLAINet achieves strong accuracy and generalization performance. It achieves favorable performance on the 2025 dataset (R 2 = 0.8866, RMSE = 0.6147, rRMSE = 15.29%) and the 2023 cross-year and cross-cultivar dataset (R 2 = 0.7119, RMSE = 0.4663, rRMSE = 30.63%), surpassing all baseline methods in overall performance under both scenarios. The model is lightweight and can be deployed on edge devices for high-speed inference. Moreover, an end-to-end LAI estimation system was designed and validated in real-world scenarios. Overall, PhysLAINet shows strong potential to integrate physical priors into deep learning for precision agriculture.