# Physically-Data Driven Approach for Predicting Formation Leakage Pressure: A Dual-Drive Method
## 3 Selection, Processing, and Correlation Analysis of Training Samples
### Data Correlation Analysis and the Setting of Two Models  
The previous literature commonly utilizes correlation analysis, particularly Pearson correlation analysis, to select input layer data. Such correlation analyses generally rely on a straightforward mapping relationship between a particular type of data and the output layer data to assess the degree of correlation; however, these analyses do not take into account the underlying mechanism of the data. Hence, in this study, we initially examine the correlation between the selected input layer data and the output layer data, considering a single mapping relationship. Moreover, given that logging data frequently display non-normal distributions (as confirmed in Figure 3), Spearman correlation analysis  
Figure 6: Vertical profile of formation leakage pressure in Well M-1. is employed, as it is appropriate for non-normally distributed data [32]. The degree of correlation is determined by assessing the magnitude of the correlation coefficient. For additional information, please consult Figure 7.  
This study computed the \(p\)-values for the chosen input layer variables and the formation's leak-off pressure. All computed \(p\)-values were below 0.0001, signifying significant distinctions between the designated feature variables and the leak-off pressure. Consequently, additional scrutiny of the feature variables is imperative to select suitable input layer variables for the model. The analysis of Figure 7 reveals the correlation patterns between the input layer parameters and the formation pressure loss equivalent density (Pv), as follows: In terms of positive or negative correlation, the formation density (DEN) and equivalent pore pressure density (Pp) exhibit a positive correlation with the formation pressure loss equivalent density (Pv). Conversely, well diameter (CAL), sonic travel time (DT), natural gamma (GR), and shale content (VSH) display a negative correlation with the formation pressure loss equivalent density (Pv). When examining the absolute values of the correlation coefficients, the formation density (DEN) exhibits the weakest correlation with a coefficient of only 0.065. Well diameter (CAL) demonstrates the strongest correlation with the formation pressure loss equivalent density (Pv), followed by shale content (VSH), with both parameters displaying comparable correlation coefficients. Natural gamma (GR) and equivalent pore pressure density (Pp) exhibit slightly lower correlation coefficients, yet their absolute values remain relatively similar. Based on the aforementioned analysis, when considering the individual correlation [33] between each input layer parameter and the formation pressure loss equivalent density (Pv), well diameter (CAL), natural gamma (GR), shale content (VSH), and equivalent pore pressure density (Pp) demonstrate a moderate correlation, while sonic travel time (DT) displays a weak correlation, and formation density (DEN) exhibits no correlation. However, from a rock mechanics perspective, there exists a certain degree of association between formation density and pressure loss. Therefore, during the subsequent model construction, two different approaches will be considered:  
Scheme 1 involves retaining the formation density (DEN) data as an input layer parameter, including CAL, DT, GR, VSH, Pp, and DEN. Scheme 2 entails removing the formation density (DEN) data as an input layer parameter, consisting of CAL, DT, GR, VSH, and Pp. Figure 7: M-1 well training sample data correlation heat map (Spearman). A comparative analysis will be conducted between the two approaches during the subsequent training process to evaluate their respective performances. To mitigate the problem of gradient vanishing or exploding, it is imperative to normalize all sample data, thereby reducing dimensionality and mitigating the impact of varying parameter scales on model performance.