# Predicting Dissolution Kinetics of Tricalcium Silicate Using Deep Learning and Analytical Models
## 4 Predictions from Deep Forest Model

Table 3: \(R\), \(R^{2}\), \(MAE\), \(MAPE\), and \(RMSE\) evaluating prediction accuracy of the DF model against the testing dataset. able to significantly reduce the variance error in its output. Next, bias error is minimized by adopting the randomization at bootstrap and feature selections [59], which ensures that the output of one tree does not interfere with that of others. Lastly, the utilization of the 10-fold cross-validation method [65] and grid-search method [48; 67] autonomously optimized the hyper-parameters so as to establish optimal input-output correlations as well as account for outliers. The DF model can estimate the influence (in terms of importance) of input variables on the dissolution rate of C\({}_{3}\)S. The results of this analysis are shown in Figure 2, which is organized in descending order based on the magnitude of variables' influence. This rank is also utilized as a guide for feature selection in the development of the analytical model in Section 5. As can be seen in Figure 2, the initial pH, Ca concentration, SSA of C\({}_{3}\)S, and flow rate--ranked from high to low--exhibited the strongest influences on the dissolution rate of C\({}_{3}\)S. This is expected because the Ca and OH ions (in terms of pH value) are known to be the main factors that affect the dissolution reaction according to _IAP_ (described in Section 5) of C\({}_{3}\)S dissolution, where a high concentration of these ions significantly reduces the dissolution rate. The SSA of C\({}_{3}\)S is the third important variable because an increase in the interface between C\({}_{3}\)S particles and solvent leads to a monotonical increase of the dissolution rate [20]. Similarly, the flow rate in the _flow chamber with VSI_ method plays a significant role, as it determines the speed at which ions are leached from the surface of the C\({}_{3}\)S particles, with higher flow rates leading to an increase in the leaching speed. Temperature is also an important variable, as previous research [27] has shown that the dissolution rate of minerals increases exponentially with an increase in temperature. Other ions in the solvent contribute less significantly to the dissolution rate. This is not a surprise, because no literature has found direct correlations between C\({}_{3}\)S dissolution rate and those ions. Interestingly, the Si ion, one of the major ions that affect the dissolution rate of C\({}_{3}\)S, was ranked much lower in terms of importance. This is likely because there are only three solvents in the database that contain Si ions, and the dissolution rates for these systems show little variation. As a result, the Si ions are less important than they would be in a larger and more diverse dataset. It should be noted that the importance of input  
Figure 2: The influence (importance) of input variables based on their contributions towards the C\({}_{3}\)S dissolution rate. The permutation of the rank is shown in a descending manner, where variables on the left side have more influence. variables can vary depending on the dataset used. Some variables may be found to be more important in one dataset, while being less significant in another. In this study, only a few variables were found to have a strong influence on the dissolution rate of C\({}_{3}\)S. However, in a different dataset, different variables may exhibit a greater importance.