# Physically-Data Driven Approach for Predicting Formation Leakage Pressure: A Dual-Drive Method
## 3 Selection, Processing, and Correlation Analysis of Training Samples
### Construction, Evaluation, Comparison, and Application of the Two Approaches  
Figure 8 illustrates the schematic diagram of the LSTM-BP model constructed in this study for intelligent prediction of formation pressure loss. The model construction process, as depicted in Figure 1, encompasses data selection, data preprocessing, data normalization, dataset partitioning, determination of evaluation metrics, design of the two approaches, and model evaluation and selection. The formation pressure loss intelligent prediction models are sequentially constructed based on Approach 1 and Approach 2. Figure 9 displays the performance of the two models in terms of evaluation metrics during the training process, while Figure 10 presents the comparison between the predicted and true values on the test set. Table 2 presents the final evaluation metrics of the two approaches on the test set. \begin{table}
\begin{tabular}{c c c} \hline \hline
**NO** & **Parameters** & **Value** \\ \hline
1 & Model layers & 3 \\
2 & Number of neurons per layer & 30 \\
3 & Activation function & LeakyRelu \\
4 & Loss function & MSE \\
5 & Maximum number of & 300 \\  & iterations (epoch) & 50 \\
6 & Batch size & Randomly select 75\% of the data as the training set \\
7 & Data partitioning & and 25\% of the data as the test set. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: LSTM-BP model parameter table. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Name** & \begin{tabular}{c} **Input** \\ **Variables** \\ \end{tabular} & **MSE** & \begin{tabular}{c} **Difference** \\ **(\%)** \\ \end{tabular} & **MAE** & \begin{tabular}{c} **Difference** \\ **(\%)** \\ \end{tabular} & **R\({}^{2}\)** & \
\begin{tabular}{c} **Difference** \\ **(\%)** \\ \end{tabular} \\ \hline Option 1 &
\begin{tabular}{c} CAL, DT, GR, \\ VSH, Pp, and \\ DEN \\ CAL, DT, GR, \\ VSH, and Pp \\ \end{tabular} & 0.000229935 & 992.393 & 0.011198329 & 240.674 & 0.92178272 & 66.920 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the predictive performance of two models for Well M-1 on the test set. Figure 8: The schematic diagram of the LSTM-BP leakage pressure intelligent prediction model. Figure 10: Model training evaluation index map (Scheme 2). Figure 9: Model training evaluation index map (Scheme 1). Figures 9 and 10 illustrate significant differences in the changes of the three evaluation metrics during the initial 200 iterations between the Approach 1 and Approach 2 models. The performance of the Approach 2 model is noticeably inferior to that of the Approach 1 model across all three evaluation metrics. The Approach 1 model demonstrates greater stability and stronger predictive capability. Nonetheless, both models converge to optimal values for the evaluation metrics around 50 iterations. The evaluation metrics in Table 2 demonstrate that the Approach 1 model outperforms the Approach 2 model on the test set, displaying lower values of MSE and MAE, and a higher value of R\({}^{2}\). These results suggest that the Approach 1 model exhibits superior predictive accuracy and a greater ability to account for the variance in the true values. Therefore, for intelligent prediction of formation pressure loss, we recommend utilizing the Approach 1 model due to its superior performance in evaluation metrics and stability during the training process. Considering Figures 9-11 across the entire set of 126 test data points, the Approach 1 model exhibits a relative error range of \(-\)2.467% to 2.510%, whereas the Approach 2 model shows a broader range of \(-\)6.141% to 5.201%. These results imply that the Approach 2 model has a wider range of prediction errors and demonstrates greater fluctuations in relative errors compared to the Approach 1 model. Moreover, based on the findings presented in Table 2, it is evident that the LSTM intelligent prediction model for formation pressure loss, developed in this study, exhibits a remarkable level of prediction accuracy, as all three evaluation metrics perform exceptionally well.