## 3 Simulation Results
### Prediction Based on Static Data  
The machine methods of BOS process modeling are, in this case, based on a set of selected static data from melts. A set of 872 melts with static data (see Table 1) was divided into training and test data. The test data represented 10% of the data from the end of the whole melt set. A total of 785 melts were used for training, and 87 melts were used for testing. Note that the test data did not enter into the learning of the machine models. When applying such an approach to BOS endpoint modeling in practice, it is necessary to ensure that the set of static melting data is continuously updated or supplemented to improve prediction. The training and testing datasets were divided into input observations and possible prediction targets. Table 1 lists all selected observations and targets from the static dataset. This table shows fixed BOS observations (i.e., \(x_{1}\),..., \(x_{15}\)) and optional data. Melt temperature and carbon concentration were considered as target process variables. Melting duration as an optional target variable was not investigated in this paper. When endpoint BOS melt temperature was modeled and predicted, the endpoint carbon concentration in melt and melting duration was regarded as the next input observations (i.e., \(x_{16}\) = endpoint carbon concentration in the melt, \(x_{17}\) = melting duration). Otherwise, when carbon concentration in the melt was modeled and predicted, then melt temperature and melting duration was considered as input observations (i.e., \(x_{16}\) = endpoint melt temperature, \(x_{17}\) = melting duration). The total number of input observations in the training and testing of the machine regression models was 17. In addition, the performance impact of including lime and dolomitic lime as optional observations was also investigated. Separate tables show the performance of models with added lime. Table 4 shows the performance results of the previously described machine learning models. The endpoint BOS temperature in the melt was considered the target of modeling and prediction. The table shows the performance of the individual models from the training phase (i.e., learning) and the testing phase. In both phases, statistical indicators were calculated (i.e., see Equations (21)-(26)). These indicators express how well the models fit the measured target data. Special indicators were the training time and the performance index (PI), which expresses the overall performance of the applied model. The obtained results were contradictory. In Table 4, it can be seen that in the training phase, the machine learning model based on RF achieved the best performance (i.e., PI = 0.33). Table 5 shows the calculated relative and absolute errors of the ten selected melts from the test phase. The calculated average errors confirm the results from Table 4. The Gaussian kernel-based SVR modeling method was the second to achieve the best results (i.e., PI = 0.47). On the other hand, the NN-based regression was the worst in training (i.e., PI = 0.81). In this case, the NN had one hidden layer with 35 neurons. On the other hand, the MARS regression method with the piecewise-cubic model in the testing phase achieved the best performance (i.e., PI = 0.50). This is because the MARS model approximated target data most precisely. Regarding performance, the NN model was the least powerful in training and testing. In terms of training time, the \(k\)-NN proved to be the fastest method (i.e., training time was 0.001 s), and the regression model based on RF proved to be the slowest (i.e., training time was 64.58 s). Similarly, Table 6 presents the carbon content modeling in temperature prediction results. Unfortunately, machine learning methods were not as powerful as temperature modeling and prediction in this case. In training, the most powerful method indicated by the lowest PI was SVR with the polynomial kernel (i.e., PI = 4.68). The second-best machine learning method was RF regression (i.e., PI = 7.72).