## 4 Results and Discussion
### Development of the Optimized Prediction Model for Corn Yield
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & **GS(\({}^{\text{(1)}}\)** & **May** & **Jun** & **Jul** & **Aug** & **Sep** & **MJ(\({}^{\text{(2)}}\)** & **J(\({}^{\text{(3)}}\)** & **JA(\({}^{\text{(4)}}\)** & **AS(\({}^{\text{(5)}}\)** & **MJJ(\({}^{\text{(6)}}\)** & **JA(\({}^{\text{(7)}}\)** & **JAS(\({}^{\text{(8)}}\)** \\ \hline EVI\({}^{\text{(9)}}\) & 0.768 & 0.103 & 0.352 & 0.697 & 0.816 & 0.421 & 0.269 & 0.608 & 0.852 & 0.682 & 0.526 & 0.800 & 0.832 \\ LAI\({}^{\text{(10)}}\) & 0.376 & \(-\)0.224 & \(-\)0.078 & 0.358 & 0.456 & 0.094 & \(-\)0.155 & 0.238 & 0.471 & 0.374 & 0.156 & 0.414 & 0.462 \\ GPP\({}^{\text{(11)}}\) & 0.522 & \(-\)0.046 & 0.109 & 0.445 & 0.491 & 0.402 & 0.040 & 0.419 & 0.499 & 0.508 & 0.349 & 0.511 & 0.529 \\ PPT\({}^{\text{(12)}}\) & 0.453 & 0.155 & 0.300 & 0.263 & 0.323 & 0.153 & 0.307 & 0.339 & 0.408 & 0.327 & 0.346 & 0.453 & 0.383 \\ TMIN\({}^{\text{(13)}}\) & 0.429 & 0.415 & 0.461 & 0.193 & 0.358 & 0.385 & 0.459 & 0.363 & 0.316 & 0.427 & 0.395 & 0.380 & 0.388 \\ SM\({}^{\text{(14)}}\) & 0.499 & 0.385 & 0.448 & 0.461 & 0.495 & 0.389 & 0.542 & 0.530 & 0.545 & 0.507 & 0.461 & 0.497 & 0.487 \\ \hline \multicolumn{10}{c}{(1) Growing Season; (2) May-June; (3) June-July; (4) July-August; (5) August-September; (6) May-June-July; (7) June-July-August; (8) July-August-September; (9) Enhanced Vegetation Index; (10) Leaf Area Index; (11) Gross Primary Production; (12) Precipitation; (13) Maximum air temperature; (14) Soil Moisture.} \\ \end{tabular}
\end{table} 
Table 5: Correlation coefficients between the selected variables and soybean yields according to combinations of months, 2006–2015. propagation (RMSProp) as an optimizer. For the activation function, the ReLU outperformed the sigmoid and hyperbolic tangent functions. The drop-out ratio was set to 40% through minimization of RMSE and MAPE. Then, we examined the results of all 18 corn yield models (six models by three periods). The overall prediction accuracy was higher for JA than for GS or OC. In terms of the correlation coefficient, the highest accuracy was 0.945 for JA, 0.919 for GS, and 0.935 for OC. This suggests that a prediction model consisting of July and August input data is sufficient for corn-yield forecasting for the year. Therefore, we can forecast the yield for the year in advance (at the beginning of September) using the  
Figure 4: The results of the optimized deep neural network (DNN) model: root mean square error (RMSE) and mean absolute percentage error (MAPE) according to the (**a**) hidden layer structure, (**b**) loss function, (**c**) optimizer, (**d**) activation function, and (**e**) drop-out ratio. JA database. The summary of validation results produced by the 10 rounds of experiments between 2006 and 2015 are presented in Table 6.  
The optimized DNN model produced the highest prediction accuracy (RMSE = 0.765 ton/ha and MAPE = 7.6%), and the scatter plot of the DNN for the predicted versus actual corn yields during 2006-2015 showed better agreement than other models (Figure 5). The other five models had somewhat dispersed patterns in terms of the one-to-one line of the scatter plots, which was due to problems with overfitting or local minima. The DNN model overcame such issues because of the intensive optimization in the deep network structure, including the best configurations for the cost function, optimizer, activation function, and drop-out ratio. In terms of MAE, the DNN model with the JA database produced an approximately 21% (0.703/0.582-1) to 33% (0.773/0.582-1) better outcome than the other five models.