# Pore Water Pressure Prediction Based on Machine Learning Methods--Application to an Earth Dam Case
## 4 Results and Discussion
### Model Performance and Comparison
The convergence efficiency of MLP is much better than that of RF-SA in terms of similar accuracy, which indicates that the architecture of MLP is more suitable for the small time series database, and the corresponding optimization method is more economical and robust. Some of the studies indicate that RF is good at classification issues based on high-dimensional, small-size databases [50]. Therefore, the PWP prediction models of the other three sensors (C5, C24, CCF1) are built with MLP, as shown in Table 4. Measurements from earlier decades are still influenced by the PWP dissipation processes caused by dam construction, and this aspect is well-represented in the four prediction models. The dynamic neural networks can memorize the characters inputted by time step, and especially GRU can remember the effects more intelligently by gate units. Several gates allow us to select the most important properties and sensitively evaluate the weight sensitivity. Then, the accuracy of the model could achieve 0.97, and the MSE is less than 0.007 kPa. The ability to predict depends not only on the hyperparameters but also on the architecture. These analytical procedures and the results obtained from them are described in the next section. A higher number of epochs refers to the model completing more iterations of both forward and backward passes across all training batch sizes. This allows the model to capture more information and adjust weights from the dataset. The most proper hyperparameters (with underline) in the GRU model are shown in Table 5, which are obtained from the loop algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Sensor** & **MSE (kPa2)** & **R2** \\ \hline
1 & C2 & 0.0292 & 0.9820 \\
2 & C5 & 0.0051 & 0.9981 \\
3 & C24 & 0.0040 * & 0.9034 \\
4 & CCF1 & 0.0073 & 0.9925 \\ \hline \hline \end{tabular}  
* MSE is relatively low because PWP of C24 has a small variation compared to C2, C5, and CCF1.  
\end{table} 
Table 4: The accuracy comparison of prediction model for four piezometers (testing datasets). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & & **MSE (kPa2)** & **R2** & **CPU Training Time (s)** \\ \hline \multirow{3}{*}{MLP} & Mean & 0.0087 & 0.9949 & 8.14 \\  & Max & 0.0091 & 0.9935 & 10.35 \\  & Min & 0.0066 & 0.9912 & 7.12 \\ \hline \multirow{3}{*}{RF} & Mean & 0.021 & 0.9801 & 52.13 \\  & Max & 0.0259 & 0.9878 & 96.56 \\  & Min & 0.0194 & 0.9766 & 12.34 \\ \hline \multirow{3}{*}{RNNs} & Mean & 0.0657 & 0.9601 & 7.22 \\  & Max & 0.0799 & 0.9623 & 10.26 \\  & Min & 0.0511 & 0.9594 & 5.54 \\ \hline \multirow{3}{*}{GRU} & Mean & 0.0623 & 0.9689 & 27.16 \\  & Max & 0.0746 & 0.9717 & 37.22 \\ \cline{1-1}  & Min & 0.0435 & 0.9702 & 19.42 \\ \hline \hline \end{tabular}  
* MSE is relatively low because PWP of C24 has a small variation compared to C2, C5, and CCF1.  
\end{table} 
Table 3: Prediction performance and efficiency of ML models (both training and testing datasets). Because of the random training mechanism, the model is different every time. Therefore, the hyperparameters should be validated at least 10 times. The maximum, minimum, and statistic mean of R\({}^{2}\), MSE, and CPU running times of different models are shown in Table 3, which demonstrates the accuracy and efficiency of the prediction capability. The testing results are shown in Figure 8. The accuracy of the RF and MLP models is similar; however, the MLP is slightly more efficient than the RF-SA. From the histogram, the residual density distribution is normal, with a mean equal to zero. They both have a powerful ability to predict the PWP, which is validated by the testing simulation performance. In the feedback neural networks, the GRU model is more robust than the standard RNNs. That is because GRU is better for long-term memory than the standard RNNs. Hydraulic behavior is not only decided by recent hydrostatic events but also by the structure's evolution over several decades. For example, in the case study, early  
Static ML models perform better for interpolation rather than extrapolation.