## 5 Discussion  
In this study we highlight the advantages of BO-LSTM fusing multi-source data for winter wheat yield estimation. The results show that the deep learning model fusing multi-source data provides reliable winter wheat yield estimation at the regional scale. In general, GPP, LAI, and VIs are suitable for large-scale crop yield estimation. The estimation accuracy can be improved by combining meteorological data. The highest estimation accuracy is achieved when all predictors are combined and entered into the estimation model, which is very similar to previous studies [25; 46; 47]. Since this paper uses SVM, LSTM, and LASSO as the yield estimation models, which are regularized, we do not need to consider the problem of multicollinearity. The Bayesian optimizer can determine an acceptable value very quickly, which is especially advantageous when the time complexity of finding the value of any function of the black box function is high, and the Bayesian optimizer does not have a limit on the search fineness. The disadvantage is that the returned result is not necessarily the true minimum objective function value (grid search may not find it either), and the result of each optimization will vary. Therefore, several optimizations are needed when optimizing the LSTM hyperparameters with Bayesian, and the best optimization result is finally selected. For the problem of different estimation accuracies in different regions (Figure 6), we analysed the distribution of winter wheat cultivation over 15 years and found that we only listed four of them (Figure 7), and the distribution of wheat cultivation in Taocheng, Iizhou, Anping, and Rao Yang regions was more scattered with less cultivated area. Among them, Taocheng District and Jizhou District are the city centre of Hengshui City. The marginal effects of various factors in cities within a certain region affect climate factors, and local climate is difficult to obtain accurately compared to other regions, resulting in differences between the meteorological data we obtained and the actual meteorological data [48]. This explains the large discrepancy between estimated yields and official yield records in these areas. Our method is therefore more suitable for areas where the distribution of cultivation is concentrated, far from urban building sites, and with relatively little human interference. In the process of analysis, we found that there are still some limitations. The first is that we focus on estimating county-level crop yields, which leads to smaller training samples due to the difficulty of obtaining data. The problem of data scarcity makes the learning information aspect of the LSTM neural network model insufficient in the training process. Second, the essence of deep learning is feature extraction from data to data, and neural network modelling converts the original input variables into high-level representations through nonlinear activation and squeeze functions. The description and mechanistic expression of the crop growth process cannot be learned, which weakens the traceability and interpretability of the LSTM model. The data-driven crop growth model has great potential. The crop growth model can take the crop, environment, and cultivation technology as a whole. The principles and methods of systems analysis can be applied to provide theoretical generalizations and quantitative analyses of the physiological processes of crop growth and development, photosynthetic production, organogenesis, and yield formation and their feedback relationships to environment and technology. Following that, the corresponding mathematical models are developed to carry out the dynamic quantitative simulation of the crop growth process. Therefore, fusing deep learning with crop mechanism models can improve the interpretability of deep learning models. To address the problems, our future work focuses on expanding the study area to integrate process-based models and deep learning techniques to develop hybrid models.