Nitrogen (N) and potassium (K) are key elements for crop growth, yet studies on the impact of N–K interactions on plant N and K status and yield are lacking.  This study aimed to develop effective indicators for diagnosing N and K nutrition and predicting the yield of wheat under N–K interactions based on the theoretical framework of a critical nutrient dilution curve.  A 4-year N–K interaction experiment involving three wheat cultivars was employed for building and validating nutrient indices (NIs) based on the critical N dilution curve (CNDC) and the critical K dilution curve (CKDC).  In addition, relevant data from the literature were collected for supplementary validation.  The results revealed that changes in parameter A1 of the critical K dilution curves (CKDCs) can reflect the impact of nitrogen application on K absorption and utilization.  However, the difference in K nutrition index (KNI) values calculated by CKDC under different N levels was not significant.  Based on the aboveground biomass (AGB), a universal CKDC was established and defined as K_c=3.63AGB^–0.37 under N–K interactions.  The results showed that the direct effects of N or K deficiency on crops could be quantified by the N–K interaction index (NKI) calculated by integrating CNDC and CKDC, and the changes in crop growth in response to proportional N and K concentrations could be determined by NKI as well.  In addition, topdressing N fertilizer at the jointing stage significantly improved the N–K interaction effect on the N nutrition index (NNI) and NKI at the booting stage (P<0.05), but it had no significant N–K interaction effect on the KNI.  All indicators at the heading stage demonstrated the best predictive capability for relative yield (RY) compared to other stages.  Compared with NNI and KNI, the prediction accuracy of yield with NKI improved by 11.63 and 17.44%, respectively.  The NKI has better performance in diagnosing N and K nutrition and predicting yield under N–K interactions than either NNI or KNI.  This result enhances our understanding of the effects of N–K interactions on wheat growth and has important applications for improving the accuracy of N and K nutrition diagnosis and yield prediction.

Estimating wheat yield is crucial for the quality of life and food security of a nation, particularly when crops face lodging stress, which severely hinders photosynthesis and maturation, resulting in yield loss.  Rapid and accurate yield estimation is essential for disaster assessment and subsequent agricultural management.  This study utilizes spectral, structural, and temperature data to comprehensively analyze the differential performance of multi-source data under two scenarios, selecting parameters that effectively represent yield differences under stress conditions.  It also explores how the introduction of a specific parameter (the lodging index) affects the prediction accuracy of six wheat yield estimation models: eXtreme Gradient Boosting (XGBoost), Ridge Regression (RR), Random Forest Regression (RFR), K-Nearest Neighbors (KNN), Support Vector Regression (SVR), and Stacking Ensemble Learning (SEL).  Compared with traditional models, the SEL model had the highest average prediction accuracy at 3 days after lodging (R²=0.64), 12 days after lodging (R²=0.70), and with combined multi-temporal features (R²=0.73).  With the introduction of the lodging index, the prediction accuracy of all models improved to different degrees, and the SEL model showing an average R² increase of 8.19, 5.09, and 6.17%, respectively.  Combined with the transfer learning methods such as transfer component analysis (TCA), joint distribution adaptation (JDA), and balanced distribution adaptation (BDA), the model maintained stable accuracy even with only 4% of the target dataset supplemented, achieving a high transfer prediction performance (R²=0.81).  By optimizing the dataset under lodging stress scenarios and integrating ensemble learning and transfer learning techniques, the accuracy, stability, and transferability of wheat yield estimation models under lodging stress were effectively improved, providing a reference for wheat disaster assessment and the formulation of remedial measures.