# Predicting Dissolution Kinetics of Tricalcium Silicate Using Deep Learning and Analytical Models
## 2 Database Collection  
The C\({}_{3}\)S dissolution database used in this study consists of 292 data records, which were consolidated from [PERSON] et al. [37; 38] and [PERSON] [39]. However, these data records are not compatible with our database due to differences in experimental parameters. For example, [PERSON] et al. [54] measured the dissolution rate of C\({}_{3}\)S at the induction period and later ages; [PERSON] et al. [55] and [PERSON] et al. [56] used the filter dissolution technique; and [PERSON] et al. [57] used the face-specific dissolution method to measure the dissolution rate of C\({}_{3}\)S. The database used in this study contains 11 input parameters: temperature (\({}^{\circ}\)C); specific surface area (SSA) of C\({}_{3}\)S (m\({}^{2}\)/g); flow rate (mL/min/mm\({}^{2}\)) initial concentration of Na, Cl, Ca, Si, Cs, K, and SO\({}_{4}\) (mM); and initial pH (unitless). The output is the dissolution rate of C\({}_{3}\)S (umol/m\({}^{2}\)/s). There are 92 data-records from [PERSON] et al. [37; 38] measured by the _reactor connected to ICP spectrometer_ method. Since the flow rate is not applicable in this method, it was set as 0. Several solvents with different ions were utilized in the _reactor connected to ICP spectrometer_ method. There were 200 data records from [PERSON] [39] measured with the _flow chamber with VSI_ method. Moreover, since the SSA of C\({}_{3}\)S is not applicable in this method, it was set as 0. The solvents only contained calcium ions at different concentration levels. Four statistical parameters associated with inputs and output of the C\({}_{3}\)S dissolution database are summarized in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Attribute** & **Unit** & **Min.** & **Max.** & **Mean** & **Std. Dev.** \\ \hline Temperature & \({}^{\circ}\)C & 10 & 60 & 21.07 & 5.437 \\ SSA of C\({}_{3}\)S & m\({}^{2}\)/g & 0 & 0.400 & 0.112 & 0.171 \\ Flow Rate & mL/min/mm\({}^{2}\) & 0 & 1273 & 79.22 & 201.8 \\ Initial Na Concentration & mM & 0 & 1000 & 29.19 & 101.5 \\ Initial Cl Concentration & mM & 0 & 1000 & 18.74 & 113.6 \\ Initial Ca Concentration & mM & 0 & 20 & 5.824 & 6.561 \\ Initial Si Concentration & mM & 0 & 0.876 & 0.006 & 0.062 \\ Initial Cs Concentration & mM & 0 & 1000 & 5.513 & 65.45 \\ Initial K Concentration & mM & 0 & 1000 & 5.513 & 65.45 \\ Initial SO4 Concentration & mM & 0 & 200 & 8.904 & 34.95 \\ Initial pH & Unitless & 6.516 & 13.09 & 10.69 & 2.316 \\
**C\({}_{3}\)S Dissolution rate** & **umol/m\({}^{2}\)/s** & **0.3800** & **154.6** & **27.92** & **32.61** \\ \hline \end{tabular}
\end{table}
Table 2: Four statistical parameters pertaining to the 12 parameters (11 inputs and 1 output in bold) of the C\({}_{3}\)S dissolution database. The database consists of 292 unique data records.  
The ML model was trained by 219 randomly selected data records from the original database. The remaining 73 data records were used to validate the performance of the model. The prediction performance was evaluated by five statistical parameters: mean absolute error (_MAE_); coefficient of determination (\(R^{2}\)); mean absolute percentage error (_MAPE_); Pearson correlation coefficient (\(R\)); and root mean square error (_RMSE_).