## 3 Results and Discussion
### Predictive Performance of ANN Model  
Contrary to initial expectations, excellent results were obtained with an RMSE of 18.6 ppm in a simple structure using one hidden layer with five neurons. When there were 10 and 15 neurons in one hidden layer, the RMSE was 73.6 ppm and 43.8 ppm, respectively, which gave poor results. The structure with three hidden layers showed the best results in the multilayer neural network (10-15-15); the RMSE was 17.9 ppm, which did not improved the performance significantly compared to the structure having one hidden layer. Figure 6a,b shows the decbarurization curves using the measured values of the TDLAS analyzer and the prediction results of the ANN model for them. Although the prediction results of the ANN model followed the decbarurization curves well, the prediction values at the beginning of the operations were somewhat unstable. In particular, the initial values of the prediction curves often did not match the actual initial carbon concentrations already known from the measurements. A reason for this result was that we could not constrain the model so that the predicted value at the start of operation was the same as the actual initial carbon concentration. It will be possible to improve the predictive performance in the early stages of operations by training the model using data under various conditions. However, since this study focuses on the prediction of the endpoint carbon concentration, we leave it as a future challenge to improve the prediction performance in the early stages of operation. At about 4 min after the start of operation, the predicted value of the ANN model showed a plateau, though the decbarurization curve continued to decrease. Generally, the decbarurization curves plateau when the second decbarurization occurs (Figure 3a). The reason why the prediction error was relatively large around 4 min after the start of operation was because the model predicted that the secondary decbarurization occurred during this period. The decbarurization curve of Figure 6a shows no secondary decbarurization and Figure 6b shows the occurrence of secondary decbarurization in the short term. In order to accurately predict the secondary decbarurization period, it seems that additional training using more diverse data is needed. Interestingly, in Figure 6b, even though we did not consider the amount of added carbon when calculating the decbarurization curves, some operations showed that the predicted values of the ANN model increased near the time of carbon addition. These results assumed that the predictive model had been trained to adjust the intermediate \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Processing Time**} & \multicolumn{2}{c}{**Error in Operations**} & \multicolumn{2}{c}{**Error in Operations**} \\  & **without Carbon Addition** & **with Carbon Addition** & **with Carbon Addition** \\ \cline{2-5}  & **Mean** & **Std. Dev.** & **Mean** & **Std. Dev.** \\ \hline \(<\)10 min & 19.44 ppm & 17.29 ppm & 22.45 ppm & 20.58 ppm \\ \(\geq\)10 min & 2.72 ppm & 3.08 ppm & 3.77 ppm & 4.90 ppm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Accuracy of the decbarurization curves according to the carbon addition and operation time. The prediction error means the difference between the output of the decbarurization curve and the actual amount of dissolved carbon obtained through sampling. carbon concentration using the input information about the added carbon to follow the final carbon concentration. Figure 7 shows the error distributions between the actual dissolved carbon concentration at the end of decarburization of the RH process and the predicted values of the prediction model for the test data. In Figure 7a, the errors between the measured and predicted values of the endpoint carbon concentration were within \(\pm\)10 ppm. The Pearson coefficient of correlation was 0.436, which means a moderate correlation between measured and predicted values. In general, it shows that the predicted value is larger than the actual measured values.