## 3 Results
### Prediction by Deep Neural Network Regression Model  
Figure 5 shows the loss curve of the DNN model. The loss is calculated using MSE, but the unit differs from the actual value due to variable normalization during the training process. Since the dataset was divided into a training set and a test set at a ratio of 8:2, and cross validation was performed by dividing the training set into five. The training loss is the average value of five validation losses. The test loss is observed to be higher than the training loss, and this shows that overfitting is not present [38]. Table 7 summarizes the performance of the DNN regression model. The results show that DNN models outperformed the multiple regression analysis models for both WC and \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Inputed** **Variables**} & \multirow{2}{*}{**Dependent Variable**} & \multirow{2}{*}{**Dataset**} & \multicolumn{6}{c}{**Metrics**} \\ \cline{4-9}  & & & **MAE** & **MAPE** & **R** & \(\mathbf{R^{2}}\) & **MSE** & **RMSE** \\ \hline \multirow{4}{*}{Skewness **Kurtosis**} & \multirow{4}{*}{Water content (\%)} & A & 1.39 & 33.1 & 0.96 & 0.92 & 2.92 & 1.71 \\ \cline{3-9}  & & B & 1.82 & 17.9 & 0.94 & 0.89 & 4.85 & 2.20 \\ \cline{3-9}  & & C & 1.42 & 9.9 & 0.88 & 0.77 & 3.34 & 1.83 \\ \cline{3-9}  & & A, B, C & 3.08 & 48.9 & 0.79 & 0.62 & 14.11 & 3.76 \\ \cline{3-9}  & & A & 0.45 & 4.4 & 0.91 & 0.83 & 0.32 & 0.56 \\ \cline{3-9}  & & B & 0.54 & 4.9 & 0.91 & 0.83 & 0.47 & 0.68 \\ \cline{3-9}  & & C & 0.55 & 4.7 & 0.95 & 0.91 & 0.46 & 0.68 \\ \cline{3-9}  & & A, B, C & 1.09 & 9.6 & 0.67 & 0.45 & 1.84 & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Result of multiple regression analysis using features from soil surface images. Figure 5: Loss curve of deep neural network regression model: (**a**) for soil water content prediction; (**b**) for bulk density prediction. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Features** & Skewness & Kurtosis & Contrast & Correlation & H4 & H5 & H6 \\ \hline
**VIF** & 1.7 & 1.5 & 3.2 & 2.6 & 1.3 & 1.6 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Variance inflation factor of features for multiple regression analysis. BD prediction. Among the three sampling points, point C had the best performance for WC prediction, with an RMSE of 1.14%. For BD prediction, point A had the best performance, with an RMSE of 0.45 kN/m\({}^{3}\). When using the combined dataset (A, B, C), the DNN models still performed better than the multiple regression analysis models, with an MAPE of 16.9% for WC prediction and 5.7% for BD prediction. However, the accuracy of the DNN models decreased slightly when using the combined dataset compared to using individual datasets, indicating that the DNN models may perform better with more specific and focused datasets. Overall, the DNN models provided more accurate prediction for both WC and BD than the multiple regression analysis models, demonstrating the potential usefulness of DNN models in soil analysis and prediction. Figures 6 and 7 show the scatter plot of prediction results. During training of the DNN regression model, the entire dataset was divided into a training set and a test set at a ratio of 8:2, so the data from multiple regression analysis were shown about five times larger than those from the DNN. Based on the evaluation metric, the DNN model demonstrated superior performance compared to the results obtained through multiple regression analysis. This is evident even when looking at the scatter plot of the predicted and observed values. In particular, when the entire dataset was used, the multiple regression analysis produced significantly higher variance in the prediction results, leading to lower accuracy. On the other hand, the DNN model displayed a relatively impressive performance.