## 3 Results and Discussion  
### Model Development and Evaluation  
The present study, three alternative regression models namely RF, GBR, and XGBoost were used to predict the DC of CO\({}_{2}\) in brine system. The models were evaluated for their effectiveness and accuracy in predicting DC considering three input parameters including pressure, temperature, and salinity. To evaluate the performance of the developed models, different statistical metrics such as the R\({}^{2}\), RMSE, and MAE were calculated and reported in Table 4 for both test and train dataset. To obtain reliable results, the dataset was divided into 80% for training and 20% for testing and all models were optimized through hyperparameters tuning to further ensure the reliability of the developed models. Figure 6 demonstrates the performance of the developed models using clustered column charts, for all three-performance evaluation metrics (R\({}^{2}\), RMSE, and MAE), highlighting their predictive capabilities and reliability for both the test and train dataset.  
The hyperparameters for each ML model were tuned to enhance accuracy and generalization. The optimized parameters are summarized in Table 5. RF model employed 500 estimators, a maximum depth of 10, and \"auto\" for feature selection, achieving robust performance. XGBoost utilized 500 estimators, a learning rate of 0.05, and a maximum depth of 3 to effectively capture non-linear patterns in the dataset. GBR incorporated advanced regularization with 1000 estimators, a learning rate of 0.03, and a subsample ratio of 0.8, balancing flexibility and generalization of the model. All models demonstrated  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Set** & **MAE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{3}{*}{RF} & Train & 0.10 & 0.02 & 0.96 \\  & Test & 0.11 & 0.03 & 0.95 \\ \cline{1-1}  & Train & 0.18 & 0.16 & 0.973 \\ \cline{1-1}  & Test & 0.19 & 0.026 & 0.925 \\ \cline{1-1} XGBoost & Train & 0.12 & 0.184 & 0.964 \\ \cline{1-1}  & Test & 0.13 & 0.389 & 0.91 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance metrics for RF, GBR, and XGBoost models.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **Expression** & **Description** & **Good Range** \\ \hline \multirow{8}{*}{Coefficient of Determination (\(R^{2}\))} & \multirow{8}{*}{\(R^{2}=1-\frac{\sum_{i=1}^{N}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i=1}^{N}(y_{i}- \hat{y})^{2}}\)} & Measures the proportion of variance in observed data explained by the model. Higher values (closer to 1) indicate a better fit. \(R^{2}=1\) represents perfect fit, while \(R^{2}=0\) indicates no explanatory power. & \\  & & Reflects the average magnitude of prediction errors, penalizing larger deviations more heavily. Lower values indicate better accuracy. & RMSE \(\rightarrow\) 0.15 (Lower is better accuracy. & \\ \cline{1-1} \cline{2-4}  & & & Reflects the average absolute difference between predicted and observed values. Less sensitive to outliers than RMSE. Lower values indicate better performance. & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of evaluation metrics used to assess model performance.  
excellent predictive accuracy, with RF achieving the highest R\({}^{2}\) of 0.96 and 0.95 for the train and test dataset, respectively.  
Among all ML models developed in this study, the RF model emerged as the most effective overall, from R\({}^{2}\) and RMSE point of view, as represented in Figure 6c and Table 5. The RF model outperformed the XGBoost and GBR models, delivering superior evaluation metrics that demonstrated higher accuracy and better performance for both test and train datasets.