## 3 Simulation Results
### Prediction Based on Dynamic Data
Table 19 shows how the performance of machine models has changed in temperature modeling and prediction. On the second side, Table 20 shows how performance has changed in the case of carbon modeling and prediction. By comparing the results from Table 19 with the values presented in Tables 14 and 15, it can be seen that the temperature prediction performance on the training data increased in the case of using oxygen as an additional observation in the SVR model with the polynomial kernel, SVR with the Gaussian kernel, NN, piecewise-cubic MARS model and \(k\)-NN. Hydrogen increased performance only in the case of the NN model and the piecewise-cubic MARS model. In the case of adding oxygen and hydrogen as two additional observations, the training performance increased in the SVR model with a Gaussian kernel, NN, piecewise-cubic MARS model, and \(k\)-NN. In other cases, no increased prediction performance on the training data was recorded. Figure 21: Prediction of carbon concentration in the melt from dynamic observations by (**a**) SVR model with polynomial kernel, (**b**) SVR model with Gaussian kernel, (**c**) NN model, (**d**) \(k\)-NN model, (**e**) RF model. In the test phase, individual methods were applied to ten meltings, where the temperature at the endpoint was predicted. In Table 19, only the average relative error and the average absolute error at the endpoints from the ten meltings are given. An increase in performance in the case of added oxygen was noted in the NN and piecewise-cubic MARS model. In the case of added hydrogen, the performance increased in the SVR model with the Gaussian kernel and the NN model. In the case of adding oxygen and hydrogen as two additional observations, the performance in testing increased only with the NN model. By comparing the results from Table 20 with the values presented in Tables 16 and 17, it can be seen that the carbon prediction performance on the training data increased when oxygen was used as an additional observation in the case of the SVR method with the polynomial kernel, Gaussian kernel, and NN. The use of only hydrogen increased performance in the SVR model with Gaussian kernel and RF-based model. In the case of adding oxygen and hydrogen as two additional observations, the training performance increased for SVR models with the polynomial kernel, Gaussian kernel, and NN. In other cases, no increased prediction performance was noted on the training data. Similarly to temperature, in the test phase, individual methods were applied to ten meltings where the concentration of carbon in the melt at the endpoint was predicted. An  
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \multicolumn{2}{c}{**Method**} & \multicolumn{2}{c}{**Added Observational**} & \multicolumn{4}{c}{**Training**} \\ \hline  & & & **Time (6)** & \(\gamma\) & \(\gamma\) & \(\gamma\) & **MSE** & **RMSE** (5) & **MAPE (5)** & **F** & **Average Relative Error in Endpatient (5)** & **Average Absolute error in Endpatient (5)** \\ \hline SVR & \(\{\)  
increase in performance was only noted in the SVR model with a Gaussian kernel using hydrogen as another observation. In the other models, the prediction performance on the test data did not increase.