## 4 Results and Discussion  
### Experiments under Drought Conditions  
The nationwide drought of the US in 2012 caused severe crop damage, reducing corn yields by about 22.5%. We tested corn yield predictions using the six AI models and the spatiotemporal match-up database to explore how this drought affected the accuracy of yield predictions. Table 4 summarizes the result of the blind test for 2012, in which the nine-year data set (excluding 2012) was used for training, and the data set of 2012 was used for validation. The MARS, SVM, RF, ERT, and ANN models  
Figure 4: Hyperparameter optimization for the deep neural network (DNN) model of this study. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Hyperparameters (Optimized)** & **Library Used** \\ \hline MARS (1) & Pruning method: backward & earth library in R \\ \hline SVM (2) & Kernel function: Gaussian radial basis function & e1071 library in R \\ \hline RF (3) & Number of trees: 500 & \\  & Number of variables used for splitting nodes: n/3 & randomForest library in R \\  & (n is the number of input variables) & \\ \hline  & Number of trees: 500 & \\  & Number of variables used for splitting nodes: n/3 & extraTrees library in R \\  & (n is the number of input variables) & \\ \hline ANN (5) & Number of hidden units: 3 & nnet library in R \\ \hline  & Hidden units: 300–300 & \\  & Loss function: Sum of Squared Errors (SSE) & \\ DNN (6) & Activation function: Rectified Linear Unit (ReLU) & tensorflow library in Python \\  & Optimizer: Adaptive Gradient (AdaGrad) & \\  & Dropout ratio: 40\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyperparameters and libraries used for the six AI models in this study. showed the mean absolute error (MAE) between 0.975 and 1.153 ton/ha and the root mean square error (RMSE) between 1.248 and 1.643 ton/ha. In contrast, the DNN model had much lower prediction errors: an MAE of 0.666 ton/ha and an RMSE of 0.828 ton/ha, with 51% (i.e., [1.248 \(-\) 0.828]/0.828) to 98% (i.e., [1.643 \(-\) 0.828]/0.828) better performance than the other five models in terms of RMSE. The mean absolute percentage error (MAPE) of the DNN model was 12.9%, and the correlation coefficient was 0.954, which can be interpreted as an excellent accuracy even under a natural disaster situation. Actual and predicted corn yields for the study period are compared in Figure 5, in which red dots indicate 2012 data (severe drought) and black dots indicate all other years. The DNN model resulted in smaller errors and showed more concentration around the 1:1 line. However, the other five models showed more scatter around the 1:1 line and slight overestimation. This overestimation of the other models was because of the failure to cope with the unexpected drought conditions of 2012. Despite the sudden drought, the predicted corn yields of the DNN model were very close to the yield statistics, which indicates that our DNN model successfully overcame the overfitting problem and dealt with outliers appropriately. Maps for actual and predicted corn yields and the prediction errors from the leave-one-year-out blind tests for 2006-2015 are illustrated in Figure 6. The year 2012 for a drought case showed lower corn yields than the other usual years, but the accuracy was similar to that of the other usual years. Indeed, a larger database can increase the performance and reliability of DNN models. Our database was limited to 10 years because the official maps for crop type were provided since 2006 for our study area. Although the data size was not sufficient, we conducted a sensitivity test according to the size of the training set. We had nine years for the period between 2006 and 2015, except for the year 2012 for a drought case. So, we extracted different combinations of three years (9C3), five years (9C5), and seven years (9C7) from the nine years. As presented in Table 5, 20 experiments for each group were carried out.