## 4 Results and Analysis
### Comparison with Other Methods  
The analysis in the previous section led us to conclude that the highest accuracy in winter wheat yield estimation can be achieved by integrating all data, so we used data with \"GPP + Climate + LAI + VIS\" as the final input data for the BO-LSTM. To further evaluate the yield estimation performance of the BO-LSTM, we used a machine learning SVM and a linear regression Lasso to estimate the yield of winter wheat. Figure 5 presents a scatter plot of our yield estimates and statistical annals for all county test data for Hengshui city using the three prediction models. Based on the R\({}^{2}\) and RMSE values, it can be intuitively seen that the SVM (RMSE = 185.7 kg/ha, R\({}^{2}\) = 0.80) and BO-LSTM (RMSE = 177.8 4 kg/ha, R\({}^{2}\) = 0.82) model methods perform significantly better than Lasso (RMSE = 214.5 kg/ha, R\({}^{2}\) = 0.76). The potential reason could be that SVM and BO-LSTM methods capture the complex and nonlinear relationships between input variables and winter wheat yield better than linear regression models. Further, it is found that the BO-LSTM model slightly outperformed the SVM method in estimating winter wheat yield in Hengshui City. This is largely attributed to the fact that machine learning non-temporal models focus on information extraction for unordered data and do not optimize the structure for temporal data. The LSTM is a recurrent neural network structure that transmits cumulative effective information during different growth stages. It is similar to the growth process characteristics of crops: crop growth and progressive developmental changes and biomass accumulation. The effects of environmental factors on winter wheat yield are complex and non-linear. The LSTM inputs the observations into the model network structure in a temporal order, and the gate mechanism is set internally. The weights of input gates, forgetting gates, and input gates are trained to achieve automatic screening and fusion of timing features.  
Immediately afterwards, we used the BO-LSTM with better estimation accuracy and SVM to estimate winter wheat yield for all counties in Hengshui (Figure 6). In general, there was some spatial variation in the estimation advantage of different regions. The estimation performance of BO-LSTM was still slightly higher than that of SVM, regardless of the county region. Using the BO-LSTM model with better yield estimation accuracy, we can see that the RMSE is more than 300 kg/ha in RaoYang County, Jizhou City, Taocheng District, Anping County, and Fucheng County. The highest is in Rao Yang County with an  
Figure 4: Winter wheat yield estimation using BO-LSTM for different combinations of data source inputs.  
RMSE of 444. 77 kg/ha and a MAPE of 6.18. The areas with RMSE between 200-300 kg/ha are Shecheng County, Jing County, Shenzhou City, and Zaojiang County. Areas with RMSE less than 200 kg/ha include Wuyi County and Wuqiang County, with the smallest being located in Wuyi County (RMSE = 117.30 kg/ha, MAPE = 1.64).  
Figure 5: Performance of the 2005–2019 test set for winter wheat yield estimation in different forecasting models.  
Figure 6: BO-LSTM performance of yield estimation for all counties in Hengshui city: (**a**) RMSE; (**b**) MAPE.