## 5 Experimental Results
### Comparison of the Proposed Methodology with Other Analysis Methods  
The proposed method was compared with the existing equation-based carbonation model, wherein the model equation was developed using the same dataset as the carbonation coefficient according to Equation (1). Although previous studies have calculated the coefficient, the coefficient calculated in this study was optimized for the data to obtain the highest possible performance index. Because each region exhibited different environmental conditions, carbonation equations and the performance indicators for the three regions were generated separately. Table 6 summarizes the test results. The coefficients of determination of the equation-based carbonation model were 0.035, 0.129, and 0.016 for Regions A, B, and C, respectively; conversely, the coefficients of determination of the proposed carbonation model were 0.426, 0.542, and 0.677 for Regions A, B, and C, respectively. Therefore, the proposed model exhibited a higher performance index than that of the equation-based carbonation model.  
The proposed method was compared with other regression analysis methods, including linear regression, regression trees, support vector machines, and Gaussian process regression. All regression analysis methods used the same training and validation datasets. Table 7 summarizes the performance results of the different regression analysis methods. The method with the highest coefficient of determination (0.4310) among the regression analysis methods was the rational quadratic with Gaussian process regression. The proposed carbonation model exhibited a coefficient of determination that was 16.8% higher than that of the Gaussian process regression.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Region** & **Methodology** & \(R^{2}\) & **RMSE** \\ \hline \multirow{3}{*}{A} & Proposed model & 0.426 & 4.970 \\ \cline{2-4}  & [PERSON]’s second law equation & 0.035 & 6.411 \\ \hline \multirow{3}{*}{B} & Proposed model & 0.542 & 5.556 \\ \cline{2-4}  & [PERSON]’s second law equation & 0.129 & 7.377 \\ \hline \multirow{3}{*}{C} & Proposed model & 0.677 & 5.132 \\ \cline{2-4}  & [PERSON]’s second law equation & 0.016 & 8.793 \\ \hline \hline \end{tabular}
\end{table}
Table 6: LSTM model layer for the carbonation model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Regression Analysis Method**} & \multicolumn{2}{c}{**Validation Dataset**} \\ \cline{2-3}  & \(R^{2}\) & **RMSE** \\ \hline \multirow{3}{*}{Linear regression} & Linear & 0.1322 & 7.260 \\ \cline{2-3}  & Interaction linear & 0.2203 & 6.898 \\ \cline{2-3}  & Robust linear & 0.1302 & 7.373 \\ \cline{2-3}  & Stepwise linear & 0.2102 & 6.928 \\ \hline \multirow{3}{*}{Tree} & Complex tree & 0.3877 & 6.157 \\ \cline{2-3}  & Medium tree & 0.3367 & 6.363 \\ \cline{2-3}  & Simple tree & 0.2161 & 6.932 \\ \hline \multirow{3}{*}{Support vector machine} & Linear & 0.1259 & 7.537 \\ \cline{2-3}  & Quadratic & 0.2457 & 6.868 \\ \cline{1-1} \cline{2-3}  & Cubic & 0.2229 & 7.182 \\ \cline{1-1} \cline{2-3}  & Fine Gaussian & 0.3756 & 6.220 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Carbonation model prediction results of other regression methods.