## 5 Evaluation and Application of the PA-LM Model
### Evaluation of the PA-LM Model  
According to the aforementioned results of PCC, the liquid production rate, reservoir permeability, oil saturation, porosity, well length, well spacing, steam temperature, and reservoir initial temperature were highly related to the COP of horizontal CSS wells. Therefore, the aforementioned eight parameters were selected as the input variables, and the corresponding COP was utilized as the output variable for the model. Based on the initial values of the input variables and the corresponding output variable (COP), the processed values of the input variables and output variable were obtained by the data processing (Equation (2)) and used as the initial data set. To build the PA-LM model and verify its reliability, 80% and 20% of data were randomly selected from the initial data set as a training set and a testing set. The key parameters used in the PA-LM model are shown in Table 3.  
During the training process, the hyperparameters of the LM model were optimized by the PA until the \(T_{\text{max}}\) was reached. Figure 7a presents the loss decline curves of the LM and PA-LM models in the training processes. As shown in Figure 7a, the MPAE values of the PA-LM model decrease with the increase in the number of epochs, confirming that a reliable PA-LM model for the testing process was formed. A comparison of the loss decline curves shown in Figure 7a indicates that the MAPEs stabilize at 267 and 304 epochs and the final MAPEs are 2.34% and 7.68% for the PA-LM and LM models, respectively. Therefore, the PA-LM model has a faster convergence rate and a higher accuracy than the LM model because the PA effectively improved the prediction accuracy. Figure 7b shows that the loss decline curves of the LM model and PA-LM model in the testing processes have a similar trend with those in the training processes. The Clarke error grid method was also used to further verify the reliability of the PA-LM model [15]. The results from Figure 8 show that, for the LM model, 97.2% of the paired points were in the acceptable zones A, 2.1% in B, and 0.7% in zone C and D. No paired point ended up in zones E or F. For the PA-LM model, 100% of the paired points were in zone A, which was significantly more compared with the LM model. There were no paired points in zone B, C, D, or E. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters of the LM Model** & **Values** \\ \hline \(n_{1}\) & 250 \\ Number of input variables & 8 \\ Number of output variables & 1 \\ \(n_{2}\) & 200 \\ \(m\) & 15 \\ \(L\) & 0.01 \\ Loss function & MAPE \\ Optimizer & Adam \\ \(M\) & 400 \\ \(P\) & 20 \\ \(F\) & 0.8 \\ \(D\) & 0.3 \\ \hline
**PA Parameters** & **Values** \\ \hline \(n\) & 20 \\ \(c_{1}\) and \(c_{2}\) & 1.5 \\ \(T_{\text{max}}\) & 300 \\ \(r\) & [0, 1] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The key parameters used in the PA-LM model. The paired points in zone A mean that the COP values predicted by the models do not deviate from the COP values determined by simulations by more than 20%. A comparison of the results in Figure 8 shows that the PA-LM model achieved a higher accuracy due to the higher percentage of paired points in zone A. In addition, four typical data were randomly selected from the initial data set and compared with those predicted by the LM and PA-LM models (Figure 9). The results show that the COP values predicted by the PA-LM model fit well. However, the COP values predicted by the LM model deviated greatly from those in the initial data set. Therefore, the PA-LM model can predict the COP of horizontal CSS wells more accurately. The four indicators of the training and testing sets for the two models, MAPE, MSE, RMSE, and \(R^{2}\), are listed in Table 4. The lower values of MAPE, MSE, and RMSE as well as the higher values of \(R^{2}\) of the training and testing sets indicate that the PA-LM model has higher accuracy than the traditional LM model. Figure 8: The Clarke error grids of the LM and PA-LM model: (**a**) LM model; (**b**) PA-LM model.