## 4 Results
### Model Performance Analysis
\begin{table}
\begin{tabular}{c c c} \hline
**Pipeline** & **Hyperparameter** & **The Best of Values** \\ \hline \multirow{6}{*}{PFS-RF} & poly\_degree & 3 \\  & n\_estimators & 500 \\  & max\_depth & 10 \\  & min\_samples\_split & 10 \\  & min\_samples\_leaf & 4 \\  & max\_features & “sqrt” \\  & bootstrap & False \\ \hline \multirow{6}{*}{PFS-NN} & poly\_degree & 2 \\  & hidden\_layer\_sizes & (\(300,200,100\)) \\  & activation function & “logistic” \\  & alpha & 0.0001 \\  & max\_iter & 3000 \\ \hline \multirow{6}{*}{PR-XGB} & n\_components & 6 \\  & learning\_rate & 0.5 \\  & n\_estimators & 200 \\  & max\_depth & 3 \\  & min\_child\_weight & 1 \\  & booster & “gbtree” \\ \hline \multirow{6}{*}{PR-NN} & n\_components & 6 \\  & n\_estimators & 600 \\  & max\_depth & 10 \\  & min\_samples\_split & 10 \\  & min\_samples\_leaf & 4 \\  & max\_features & “sqrt” \\  & bootstrap & False \\ \hline \multirow{6}{*}{PFR-XGB} & n\_components & 6 \\  & hidden\_layer\_sizes & (\(400,300,200,100\)) \\  & activation function & “tanh” \\  & alpha & 0.01 \\  & max\_iter & 3000 \\ \hline \multirow{6}{*}{PFR-XFGB} & poly\_degree & 3 \\  & n\_estimators & 400 \\  & max\_depth & 10 \\  & min\_samples\_split & 10 \\  & min\_samples\_leaf & 4 \\  & max\_features & “sqrt” \\  & bootstrap & False \\ \hline \multirow{6}{*}{PFR-NN} & poly\_degree & 2 \\  & hidden\_layer\_sizes & (\(200,100\)) \\  & activation function & “logistic” \\ \cline{1-1}  & alpha & 0.001 \\ \cline{1-1}  & max\_iter & 5000 \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._and real production. Therefore, the adopted model can be considered to have strong predictive ability. The data normalization was executed within the processing pipeline, while it did not perturb the intrinsic range of our predictive outcomes. Specifically, the production capability in the designated operational zone is expected to span between 0 to 2000 m\({}^{3}\)/d. The mathematical formulae represented in the Taylor diagram delineated in Section 2.3.2 were employed to compare the real production capacity against the forecasted values, and the outcomes are illustrated in Figure 7. The analysis reveals that the standard deviation  
Figure 6: Comparative analysis of production capacity projections using the 20% residual dataset vs. real predictions. of the baseline data stands at 192.2. Notably, every pipeline, post-training, manifests a standard deviation smaller than that of the original dataset. This suggests that the variance within the trained data across all pipelines is less pronounced than that observed in the raw data. Given the significant deviation inherent in the dataset, the RMSE values for all pipelines exceed those from previously reported data; however, they remain substantially below the observed standard deviation. This context suggests that the predictions of the model operate within an acceptable margin. In subsequent sections, the validation against the remaining 20% of the data across 33 wells will be elucidated. Table 4 presents the array of evaluation metrics as depicted in the Taylor diagram for all pipelines, offering a comprehensive view of their performance. Meanwhile, Table 5 details a standardized list of evaluation indices, serving as a benchmark for assessing all pipelines. Furthermore, in Tables 4 and 5, the \(\bigstar\) symbols located in the leftmost column are indicative of the best-performing models, highlighting the results achieved by the most effectively trained models in our analysis. In Taylor plot analysis, the discrepancy between the standard deviation of predicted production data and the standard deviation of real production data indicates the model's capacity to encompass the data's variability. Ideally, the standard deviation of the predicted production data should closely align with that of the real production data, visually positioning the model point (\(\sigma_{p}\)) near the radius of the reference points (\(\sigma_{l}\)) on the Taylor plot.