## 3 Results and Discussion
### Input Variables Significance  
To determine the effect of input parameters on DC, SHAP (Shapley Additive Explanations) values were utilized, as shown in Figure 11a. The RF model was chosen for this analysis due to its high accuracy, interpretability, and ability to manage complex relationships within data. RF effectively ranks feature importance by aggregating results across multiple decision trees [46]. When combined with SHAP values, it provides a clear explanation of each parameter's (e.g., pressure, temperature, and salinity) contribution to the target variable (e.g., DC), making it an ideal choice for accurately evaluating feature influence. As shown in Figure 11a, temperature has the most significant impact on predicting the DC, followed by salinity and pressure. Notably, salinity, a fluid-related parameter (brine), demonstrates the second-highest influence on estimating the DC.  
The \"bee swarm\" plot illustrated by SHAP values in Figure 11b ranks variables by their mean absolute SHAP values in descending order, with the most important parameters appearing at the top. Each point on the plot represents a data instance, plotted against its impact on the predicted DC value. The color of the points indicates the relative magnitude of the feature values, ranging from low (blue) to high (red). For instance, higher salinity values (red points with negative SHAP values) correspond to lower predicted DC values, demonstrating a negative relationship. In contrast, temperature, the most significant feature, shows a broader range of SHAP values, with predominantly positive impacts on  
\begin{table}
\begin{tabular}{c c c c} \hline
**Author** & **Model** & **Data Points** & **RMSE (Test)** \\ \hline \multirow{4}{*}{[PERSON] et al. (2025) [35]} & MLP & & 3.5452 \\  & CFNN & & 5.2872 \\  & RNN & 191 & 4.9287 \\  & GEP & & 5.5611 \\ [PERSON] et al. (2020) [33] & PSO-ANFIS & 86 & 0.113 \\ [PERSON] and [PERSON] & GMDH & & 0.2271 \\ [PERSON] (2020) [34] & GEP & 92 & 0.1245 \\ [PERSON] et al. (2019) [32] & MKSVM-GA & & 0.3028 \\  & RF & & 0.03 \\ \multirow{2}{*}{Current Study} & GBR & 176 & 0.026 \\  & XGBoost & & 0.389 \\ \hline \end{tabular}
\end{table}
Table 7: Comparison of ML models based on test RMSE Performance metric with current studies.  
Figure 10: Comparison of previous ML models based on test RMSE value with present study.  
DC as its value increases. Similarly, pressure exhibits a moderate influence, contributing less significantly than temperature and salinity.  
To better understand the impact of each parameter on DC and validate the results shown by RF model using Tornado and SHAP charts, dependency plots for the three key parameters were also generated using RF, which was chosen for its high accuracy. In Figure 12c, it is evident that higher salinity values have a negative impact on the DC. This aligns with the physical understanding that an increase in salinity leads to a reduction in DC [3; 27]. Additionally, since salinity inherently represents the interaction between salinity and CO\({}_{2}\), this further underscores the importance of salinity as a significant factor influencing the diffusion behavior of CO\({}_{2}\) in brine.  
Figure 11: (**a**) Tornado chart shows the importance of each parameter obtained from the RF model during hyperparameter tuning and (**b**) SHAP summary plot illustrating parameter importance.