## 3 Simulation Results
### Prediction Based on Dynamic Data
\begin{array}{llll}\text{Temperature}&(^{\circ}\text{C})=1659+0.022098\times\text{ BF1}-0.045215\times\text{BF2}-0.03343\times\text{BF3}\\ &+0.0011321\times\text{BF4}-0.0012658\times\text{BF5}+0.00012363\times\text{BF6}- 0.016099\times\text{BF7}\\ &+0.013921\times\text{BF8}-1.2843\times\text{BF9}-1.5315\times\text{BF10}+0.00218 35\times\text{BF11}\\ &+0.0016313\times\text{BF12}-0.002626\times\text{BF13}-0.18517\times\text{BF14}.\end{array}  \tag{33}\]  
When predicting from dynamic data, the aim was to determine the dynamic course of these variables, in addition to estimating the temperature and carbon at the BOS endpoint. The course of the dynamic temperature and carbon may differ for each melting. The shape of the curves depends on the model's ability to approximate the measured data and the number of actual measurements during melting that can be used to learn the model. The standard dynamic behavior was used to assess the modeled temperature and carbon (see Figure 1). Figures 20 and 21 show a comparison of temperature and carbon behavior predicted from dynamic BOS data in selected meltings by individual machine learning methods. These figures show the target variables predicted in melting #5. The black vertical line in the individual sub-figures indicates the endpoint of the melt. Qualitatively, the best temperature behavior compared to Figure 1 was achieved by the SVR model with the polynomial kernel (see Figure 20a) and the piecewise-cubic MARS model (see Figure 20e). These models achieved good accuracy at the prediction temperature at the endpoint of the melting #5 (see Table 15). Note that in the case of melting #5, the SVR model with the polynomial kernel achieved a lower endpoint error. Less smooth courses were obtained by RF (see Figure 20g), \(k\)-NN (see Figure 20f), and the SVR model with the Gaussian kernel (see Figure 20b). Although the piecewise-linear MARS model achieved the best average relative and absolute errors in the endpoint prediction, the predicted temperature's dynamic behavior was not satisfactory (see Figure 20d). Similarly, the unstable dynamic temperature profile was the output of the NN-based model (see Figure 20c). The comparison of carbon behavior predicted from dynamic BOS data by machine learning methods is shown in Figure 21. Similar to temperature modeling results, this figure shows the predicted temperature in melting #5. In comparison, the results from the MARS models are missing, as these models failed in the training phase. Graphic results show that qualitatively, the smoothest carbon behavior compared to Figure 1 was achieved by the SVR model with the polynomial kernel (see Figure 21a) and the model based on \(k\)-NN (see Figure 21d). These models also achieved the best average relative error at the BOS endpoint carbon prediction (see Table 17). Note that the \(k\)-NN model achieved a lower average endpoint error from ten selected meltings. Carbon also had a relatively smooth course in the case of simulation with a model based on NN (see Figure 21c) and RF (see Figure 21e). However, SVR obtained less smooth courses of decarbonization with the polynomial kernel (see Figure 21b). \begin{table}
\begin{tabular}{l l l l} \hline
**BF** & **Equation** & **BF** & **Equation** \\ \hline BF1 & max(0, \(x_{1}-7662.7\)) & BF8 & max(0, \(54027-x_{3}\)) \(\times\) max(0, \(0.54997-x_{1}\)) \\ BF2 & max(0, \(7662-x_{1}\)) & BF9 & max(0, \  
Figure 20: Prediction of melt temperature from dynamic observations by **(a)** SVR model with polynomial kernel, **(b)** SVR model with Gaussian kernel, **(c)** NN model, **(d)** piecewise-linear MARS model, **(e)** piecewise-cubic MARS model, **(f)** \(k\)-NN model, **(g)** RF model. Furthermore, the effect of increasing the number of input observations on the performance of individual models was investigated. Oxygen and hydrogen concentrations were used as additional input observations. Three variants of different inputs were tested, i.e., oxygen only, hydrogen, and finally, oxygen and hydrogen together.