## 6 Conclusions  
Accurate rice yield estimation is vital for food security, health issues, and agriculture trading. This study proposed the Informer model to predict district-level rice yield based on multitemporal satellite data, sequential climatic products, and historical rice yield. To evaluate the proposed Informer model, we compared the Informer model with four widely used machine learning methods, including LASSO, RF, XGBoost, and AtLSTM. Overall, the results showed that the Informer model performed best among the five models, with an average \(R^{2}\) of 0.81, _RMSE_ of 0.41 t/ha, _MAPE_ of 15.47%, and \(d\) of 0.74 from 2009 to 2016. In addition, we evaluated the performance of different models within the growing season. The proposed Informer model achieved optimal prediction (\(R^{2}\approx 0.78\)) 2 months before rice maturity. The feature importance analysis showed that NIR\({}_{\text{V}}\) was the most critical factor, while intervals 6 (mid-August) and 12 (mid-November) were the essential periods for rice yield prediction. The hidden feature analysis demonstrated that the AtLSTM model accumulated the information of each growth period, while the Informer model focused on the information around intervals 5 to 6 (August) and 11 to 12 (November). This study proposed a modeling framework to predict crop yield and explain the internal mechanism of deep learning models at the regional scale.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/rs14195045/s1](https://www.mdpi.com/article/10.3390/rs14195045/s1)]([https://www.mdpi.com/article/10.3390/rs14195045/s1](https://www.mdpi.com/article/10.3390/rs14195045/s1)). Figure S1. Scatter plots of reported yields vs. predicted yields of (a) LASSO, (b) RF, (c) XGBoost, (d) AtLSTM, and (e) Informer in four testing years: (1) 2009, (2) 2010, (3) 2011, and (4) 2012; Figure S2. Spatial patterns of the predicted yield of (a) LASSO, (b) RF, (c) XGBoost, (d) AtLSTM, (e) Informer, and (f) reported yield from (1) 2009 to (4) 2012; Figure S3. Spatial patterns of the relative errors of (a) LASSO, (b) RF, (c) XGBoost, (d) AtLSTM, and (e) Informer from (1) 2009 to (4) 2012; Figure S4. Feature importance (rescaled to 0-100) of the top 15 features from the random forest algorithm from 2009 to 2016; Figure S5. Feature importance (rescaled to 0-100) of the top 15 features from the XGBoost algorithm from 2009 to 2016; Figure S6. The attention weight distribution of the AtLSTM model from 2009 to 2016; Figure S7. Self-attention weight analysis of the Informer model in layer 1 from 2009 to 2016; Figure S8. Self-attention weight analysis of the Informer model in layer 2 from 2009 to 2016.  
Conceptualization, Y.L.; methodology, Y.L., S.W. and D.H.; formal analysis, Y.L.; investigation, Y.L.; writing--original draft, Y.L.; supervision, S.W.; writing--review and editing, S.W., J.C., B.C. and X.W.; validation, D.H. and L.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China, No. 31861143015; the Strategic Priority Research Program of the Chinese Academy of Sciences, No. XDA23100202; and the Science and Technology Planning Project of Hebei Academy of Sciences of China, No. 22A03.  
Not applicable.  
The authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work.