## 4 Results and Discussion
### Development of Optimized Prediction Model for Soybean Yield  
To examine the effect of phenology on prediction accuracy, we compared the predicted soybean yields from the GS, JA, and OC periods. The overall prediction accuracy of soybean yield was higher than for GS or OC. In terms of correlation coefficient, the highest accuracy was 0.901 for JA, 0.867 for GS, and 0.880 for OC. The validation results produced by the 10 rounds of experiments between 2006 and 2015 are presented in Table 7. The accuracy of soybean models was similar to that of corn models in terms of MAPE, but was somewhat lower in terms of the correlation coefficient. This is presumably because soybeans are a small grain and have a small yield value, which may lead to a relatively dispersed pattern around the one-to-one line on the scatter plot (Figure 6). However, the prediction results of the DNN model were relatively stable and its scatter plot was highly concentrated around the one-to-one line. Similar to the optimization of the corn yield model, the best-fitted DNN model for soybean yield was built by setting the structure of the hidden layers to 500-500 nodes, SSE for loss function, AdaGrad for optimizer, ReLU for activation function, and the drop-out ratio to be 40%. The optimized DNN model for soybean showed high prediction accuracy (RMSE = 0.285 ton/ha, MAPE = 7.8%), which suggests that the DNN approach can be also effective for crops other than corn or soybeans. In terms of MAE, the DNN model with the JA database produced an outcome approximately 17% (0.270/0.222-1) to 22% (0.259/0.222-1) more accurate than those of the other five models. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **MBE(1)** & **MAE(2)** & **RMSE(3)** & **MAPE(4)** & **Corr. (5)** \\  & **(ton/ha)** & **(ton/ha)** & **(ton/ha)** & **(\%)** & **Corr. (5)** \\ \hline MARS\({}^{(6)}\) & 0.067 & 0.773 & 1.009 & 11.0 & 0.911 \\ SVM\({}^{(7)}\) & 0.020 & 0.726 & 0.946 & 10.0 & 0.917 \\ RF\({}^{(8)}\) & 0.015 & 0.708 & 0.929 & 9.8 & 0.922 \\ ERT\({}^{(9)}\) & 0.001 & 0.703 & 0.922 & 9.6 & 0.924 \\ ANN\({}^{(10)}\) & 0.024 & 0.705 & 0.928 & 9.8 & 0.926 \\ DNN\({}^{(11)}\) & 0.029 & 0.582 & 0.765 & 7.6 & 0.945 \\ \hline \end{tabular} (1) Mean Bias Errors; (2) Mean Absolute Error; (3) Root Mean Square Error; (4) Mean Absolute Percentage Error; (5) correlation coefficient; (6) Multivariate Adaptive Regression Splines; (7) Support Vector Machine; (8) Random Forest; (9) Extremely Randomized Trees; (10) Artificial Neural Network; (11) Deep Neural Network.  
\end{table} 
Table 6: Summary of validation statistics from 10 rounds of experiments for corn yield: July–August (JA) (major productive period), 2006–2015. Figure 5: Actual versus predicted corn yields from 10 rounds of experiments for July–August (JA) (major productive period), 2006–2015: (**a**) multivariate adaptive regression splines (MARS), (**b**) support vector machine (SVM), (**c**) random forest (RF), (**d**) extremely randomized trees (ERT), (**e**) artificial neural network (ANN), and (**f**) deep neural network (DNN). \begin{table}
\begin{tabular}{l c c c c c} \hline  & **MBE(1)** & **MAE(2)** & **RMSE(3)** & **MAPE(4)** & **Corr. (6)** \\  & **(ton/ha)** & **(ton/ha)** & **(ton/ha)** & **(\%)** & **Corr. (6)** \\ \hline MARS(9) & \(-\)0.018 & 0.269 & 0.336 & 9.6 & 0.860 \\ SVM(7) & \(-\)0.036 & 0.265 & 0.339 & 9.5 & 0.850 \\ RF(9) & \(-\)0.027 & 0.261 & 0.332 & 9.4 & 0.854 \\ ER(9) & \(-\)0.030 & 0.259 & 0.329 & 9.3 & 0.859 \\ ANN(10) & \(-\)0.016 & 0.270 & 0.340 & 9.7 & 0.853 \\ DNN(11) & \(-\)0.072 & 0.222 & 0.285 & 7.8 & 0.901 \\ \end{tabular}
\end{table} 
Table 7: Summary of validation statistics from 10 rounds of experiments for soybean yield: July–August (JA) (major productive period), 2006–2015.