## 5 Conclusions  
Timely and accurate yield forecasting is important for ensuring food security and making reasonable crop planting plans. This paper tested three deep learning model architectures based on a deep learning approach to predict rice yields in Hubei Province, China. In our study, we also considered the effect of spatial heterogeneity within regions on rice yield. The performance of a custom dummy variable in rice yield prediction was evaluated. Through the experiments, we justified the research objectives and obtained the following conclusions. (1) The hybrid CNN-LSTM model performed more satisfactorily in rice yield prediction compared to the CNN and ConvLSTM models. The CNN-LSTM hybrid model had the best results on all three evaluation metrics with root mean square error RMSE = 89,878 (t), mean absolute error MAE =5 2,802 (t) and correlation coefficient R = 0.934. (2) Spatial heterogeneity has an impact on yield prediction. The self-defined dummy variables representing county numbers can improve the accuracy of rice yield prediction results.  
In considering the effect of spatial heterogeneity on crop yield, customizing the dummy variable for county numbering was only a preliminary attempt at this idea. Some improvement methods may be considered in future work by refining the effect of spatial heterogeneity on crop yield and proposing more complex features or models for representing spatial heterogeneity.  
There are also aspects of this study that could be improved in terms of yield prediction. First, only EVI, GPP, SAVI and air temperature data are used for training and prediction, but climate-related features are lacking. In the future, factors such as soil moisture, sunshine, precipitation and other factors related to rice growth can be added to the input dataset. Second, the remote sensing images are converted into normalized histograms, and the relevant spatial feature information may be lost in the histogram conversion process. In addition, in this study, we set the number of bins in the histogram to 32, and the number of bins has an effect on the training of the dataset. Future work can consider methods for combining multiple sources of data with different resolutions and time steps. Comparative experiments on the prediction effectiveness of different bin numbers can be conducted to explore the best performing histogram bin numbers. Third, modeling based on purely remote sensing data does not take into account existing crop growth models. The integration of remote sensing data with crop growth models can be considered, which may further enhance the predictive performance of the models.  
Conceptualization, S.Z., L.X. and N.C.; methodology, S.Z. and L.X.; software, S.Z.; validation, S.Z. and L.X.; formal analysis, S.Z.; data curation, S.Z.; writing--original draft preparation, S.Z.; writing--review and editing, S.Z., L.X. and N.C. All authors have read and agreed to the published version of the manuscript.  
This project was supported by the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. 2642022009), the Special Fund of Hubei Luojia Laboratory (No. 220100034), and the National Natural Science Foundation of China (No. 42201509).  
Not applicable.  
The authors declare no conflict of interest.