# 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
The aforementioned analysis reveals that the LSTM-BP-based intelligent prediction model developed in this study exhibits high accuracy and robust generalization ability, thereby holding substantial practical value for real-world production practices. Furthermore, this study deviates from the conventional approach of solely selecting input variables based on individual data correlations. Instead, it integrates the physical significance of formation density as one of the input variables, despite lacking a direct singular correlation with formation loss pressure. Nonetheless, this incorporation contributes to enhanced prediction accuracy and generalization capability of the model. This implies the significance of considering both the individual data correlation at the data level and the physical significance when selecting input variables, thereby enabling the identification of an optimal combination for the input variables. These findings offer valuable insights for the design and optimization of prediction models for formation loss pressure. These findings suggest the importance of incorporating additional physical factors associated with formation loss pressure as input variables during the construction of prediction models, thereby enhancing their predictive capacity. Simultaneously, it is essential to surpass the constraints of analyzing single data correlations and adopt a comprehensive approach that encompasses the data's characteristics and physical significance. This enables the selection of input variables that are more precise and dependable. By adopting this integrated approach that takes into account both data  
Figure 13: The comparison of input layer variables between Well M-1 and Well M-2. correlation and physical significance, the establishment and application of prediction models for formation loss pressure can be more effectively guided. Consequently, this approach facilitates the provision of more precise predictions and decision support for oilfield drilling operations. To further validate the generalizability of the conclusions drawn in the preceding text, this study employed two additional algorithms, namely, BP and random forest, to model and validate the data using Scheme 1 and Scheme 2, respectively. The outcomes are presented in Table 5. The findings revealed that, irrespective of random forest or BP, the Scheme 1 model outperformed the Scheme 2 model across all three evaluation metrics. In the case of the random forest algorithm, Scheme 1 demonstrated a decrease of 8.172% and 15.825% in MAE and MSE, respectively, compared to Scheme 2, along with an increase of 3.266% in R\({}^{2}\). In the case of the BP algorithm, Scheme 1 achieved a decrease of 2.324% and 15.636% in MAE and MSE, respectively, compared to Scheme 2, along with an increase of 16.454% in R\({}^{2}\). Moreover, through a comparison of Tables 2 and 5, it becomes evident that the LSTM-BP model developed in this study outperforms both the random forest model and the BP model.