Maize is one of the most important staple crops in the world and serves as a cornerstone of food security and agricultural sustainability. Accurate and timely prediction of maize yield is essential for optimizing agricultural management practices, supporting market regulation, and guiding policy decisions related to food supply and climate adaptation. In recent years, data-driven yield prediction methods based on machine learning and deep learning have achieved notable improvements in predictive accuracy. However, most existing approaches primarily rely on statistical correlations among variables and often treat influencing factors as independent predictors, without explicitly addressing the complex causal mechanisms and time-lagged interactions that govern crop growth processes. This limitation may lead to reduced model interpretability and compromised robustness under changing environmental conditions. To address these challenges, a novel maize yield prediction framework that integrates causal inference with a hybrid deep learning model was proposed, aiming to improve both predictive performance and mechanistic understanding.

Multi-source heterogeneous datasets collected across the maize growing season were utilized, including remote sensing-derived vegetation indices, meteorological variables（such as temperature and precipitation）, soil profile moisture measurements at multiple depths, and crop observation data corresponding to key phenological stages. First, the Peter-Clark and momentary conditional independence（PCMCI）causal discovery algorithm was applied to systematically identify causal relationships between maize yield and its potential driving factors. The PCMCI method enables the detection of both contemporaneous and time-lagged causal links while effectively controlling for confounding effects in high-dimensional time series data. Through this process, the causal structure of yield formation was explicitly characterized, and key variables with statistically significant causal impacts were selected as inputs for the prediction model. Subsequently, a hybrid moving average, convolutional neural network-long short-term memory（MA-CNN-LSTM）model was constructed to capture the complex spatiotemporal patterns in the causally screened input variables. Specifically, a moving average module was employed as a preprocessing step to suppress high-frequency noise and enhance signal stability. A CNN was then used to extract latent correlation features among multiple variables, reflecting their joint influence on yield formation. Finally, an LSTM network was adopted to model temporal dependencies and cumulative effects across the growing season, enabling effective representation of dynamic yield responses.

The causal analysis revealed that soil moisture at depths of 10 cm and 50 cm exerted a significant positive influence on maize yield（P < 0.01）, with deeper soil moisture showing a stronger and more persistent time-lagged effect. This finding highlighted the critical role of subsurface water availability in sustaining crop growth during later developmental stages. In addition, vegetation indiced such as the modified chlorophyll absorption ratio index and the normalized difference vegetation index exhibited significant short-term causal relationships with yield during the mid-growth stage of maize, indicating their sensitivity to canopy structure and photosynthetic activity during this period. Comparative experiments conducted against traditional statistical models and conventional machine learning approaches demonstrated that the proposed PCMCI-MA-CNN-LSTM framework consistently achieved superior predictive performance. On the test dataset, the coefficient of determination（R²）reached 0.955, while the mean absolute error（MAE）and root mean square error（RMSE）were reduced to 1.201 kg/mu and 1.474 kg/mu（1 hm²=15 mu）. These results indicated that incorporating causal variable selection effectively enhances model accuracy and stability by reducing redundant and spurious correlations.

The results confirm that incorporating causal analysis into yield modeling provides a robust basis for identifying key driving variables and effectively enhances the accuracy and interpretability of maize yield prediction. The proposed framework offers a promising approach for precision agriculture and decision support in crop yield forecasting, particularly under complex and dynamic agro-environmental conditions.

Maize is one of the most widely cultivated staple crops worldwide, and its aboveground biomass (AGB) serves as a crucial indicator for evaluating crop growth status. Accurate estimation of maize AGB is vital for ensuring food security and enhancing agricultural productivity. However, maize AGB is influenced by a multitude of dynamic factors, exhibiting complex spatial and temporal variations that pose significant challenges to precise estimation. At present, most studies on maize AGB estimation rely primarily on single-source remote sensing data and conventional machine learning algorithms, which limits the accuracy and generalizability of the models. To overcome these limitations, a model architecture that integrates convolutional neural networks (CNN), long short-term memory networks (LSTM), and a self-attention (SA) mechanism was developed in this research to estimate maize AGB at the field scale.

The research utilized vegetation indices, crop parameters, and meteorological data that were collected under varying gradient water treatments in the experimental area. First, an optimized CNN-LSTM-SA model was constructed. The model employed two-dimensional convolutional layers to extract both spatial and temporal features, while utilizing max-pooling and dropout techniques to mitigate overfitting. The LSTM module was used to capture temporal dependencies in the data. The SA mechanism was introduced to compute global attention weights, enhancing the representation of critical time steps. Nonlinear activation functions were applied to mitigate multicollinearity among features. A fully connected layer was used to output the estimated AGB values. Second, the Pearson correlation coefficients between influencing factors and maize AGB were analyzed, and the importance of multi-source data was validated. recursive feature elimination (RFE) was used to select the optimal input features. The local interpretable model-agnostic explanations (LIME) method was employed to interpret individual samples. Finally, ablation experiments were conducted to assess the effects of incorporating CNN and SA into the model, with performance comparisons made against random forest (RF) and support vector machine (SVM) models.

The correlation analysis revealed that crop parameters exhibited strong correlations with AGB. Among the vegetation indices, the improved normalized difference red edge index (NDREI) demonstrated the highest correlation (r = 0.63). To address multicollinearity issues, the visible atmospherically resistant index (VARI), soil adjusted vegetation index (SAVI), and normalized difference red edge index (NDRE) were excluded from the analysis. The CNN-LSTM-SA model integrated crop parameters, vegetation indices, and meteorological data and initially achieved a coefficient of determination (R²) of 0.89, a root mean square error (RMSE) of 129.38 g/m², and a mean absolute error (MAE) of 65.99 g/m². When only vegetation indices and meteorological data were included, the model yielded an R² of 0.83, an RMSE of 161.36 g/m², and an MAE of 89.37 g/m². Using a single vegetation index further reduced model accuracy. Based on multi-source data integration, RFE removed redundant features. After excluding the 2-meter average wind speed, the model reached its best performance with R² of 0.92, RMSE of 107.53 g/m², and MAE of 55.19 g/m². Using the LIME method to interpret feature contributions for individual maize samples, the analysis revealed that during the rapid growth stage, the model was primarily influenced by the current growth status and vegetation indices. For samples in the mid-growth stage, multi-day crop physiological characteristics had a substantial impact on model predictions. In the late growth stage, higher vegetation index values showed a clear suppressive effect on the model outputs. During the mid-growth stage of maize under varying moisture conditions, the model consistently demonstrated heightened sensitivity to low temperatures, moderate humidity levels, and optimal vegetation indices. The CNN-LSTM-SA model demonstrated more consistent fitting performance and accuracy across different growth stages and water conditions compared to the LSTM, LSTM-SA, and CNN-LSTM models. Additionally, it also exceeded the performance of the RF model and the SVM model in all evaluation metrics.

This study leveraged the feature extraction capabilities of CNN, the temporal modeling strength of LSTM, and the dynamic attention mechanism of the SA to enhance the accuracy of maize AGB estimation from a spatiotemporal perspective. The approach not only reduced estimation errors but also improved model interpretability. This research could provide valuable insights and references for the dynamic modeling of crop AGB.