An interpretable wheat yield estimation model using an attention mechanism-based deep learning framework with multiple remotely sensed variables

Accurate crop yield estimation enables informed decisions that support efficient and sustainable food production systems. Despite some success in crop yield estimation using deep learning models, they are often referred to as “black boxes” due to their lack of interpretability. Meanwhile, most current models are designed to provide yield estimations without assessing the uncertainty and verifying the contribution of components within the models. This work developed a novel deep learning approach to estimate winter wheat yield in the Guanzhong Plain, PR China by using three remotely sensed indices, vegetation temperature condition index (VTCI), leaf area index (LAI), and fraction of photosynthetically active radiation (FPAR) during main growth stages of winter wheat. The attention mechanism (AM) and an interpretable attribution method, backpropagation-based integrated gradients (IG), were incorporated into the deep learning approach to enhance interpretability. Additionally, to address uncertainty limitations the Monte Carlo (MC) dropout was applied to the deep learning approach to assess the uncertainty over time during data accumulation. The proposed approach (AM-CNN-LSTM) combined a one-dimensional convolutional neural network (1D-CNN) to capture local dependencies in sequences, the temporal data processing capability of long short-term memory (LSTM), and the interpretability of the AM. The AM-CNN-LSTM model had enhanced precision in yield estimation (R2 = 0.64, RMSE = 498.08 kg/ha) compared with the CNN, AM-CNN, and CNN-LSTM. The attention weights indicated that the most significant variable influencing wheat yield was FPAR, followed by LAI and VTCI. The results of IG showed that the FPAR at the jointing and heading-filling stages, LAI at the heading-filling and milk maturity stages, and VTCI at the jointing stage contributed more to the yield. The MC dropout results showed that the level of model uncertainty decreased steadily as time advanced from late March to late April and stabilized around mid-May.