## 4 Discussion of Results  
This study investigated two approaches to BOS modeling, i.e., based on static observations from a set of meltings and modeling based on joined static and dynamic data. The latter approach has not yet been studied in detail due to the need for more temperature and carbon measurements during meltings. Five machine learning methods were compared, and their performances were examined both in the training phase, i.e., target prediction on training data, and in the testing phase, i.e., prediction on unknown data that were not part of model learning. The performance of machine learning methods was evaluated using statistical indicators and calculated errors in the melting endpoint. The speed or duration of training depends on the complexity of the algorithm. The results showed that in terms of time, the slowest modeling method was based on RF, both when modeling from joined static and dynamic data and when modeling only from static data. On the other hand, \(k\)-NN regression proved to be the fastest machine learning method in both BOS modeling approaches. Machine learning speed, e.g., in the case of an online model update, may affect control interventions for the process. The RF algorithm creates as many trees on the data subset and combines all the trees' output. Hence, it reduces the overfitting problem. However, this algorithm requires much more computational power and resources. On the other hand, the fastest \(k\)-NN algorithm does not explicitly create any model, and it simply indicates new learning based on entering data from historical data. In modeling, the number of neighbors \(k\) was set to 5, but performance improvements can be found by optimizing this parameter. The MARS method proved to have the best endpoint prediction accuracy in terms of performance. The MARS model most accurately predicted temperature and carbon concentration when predicted from both static and dynamic data. The NN proved to be the least accurate model for temperature prediction from static data. The advantage of the MARS model is its relatively simple interpretation and portability. In general, MARS models worked very well on large datasets of meltings. They offer quick computation in prediction and do not require the standardization of the predictor variables. On the other hand, this algorithm proved to be more computationally intensive in training. The RF-based model best approximated training data in the case of modeling based on combined static and dynamic data and prediction from dynamic melting data. The piecewise-linear MARS model proved to have the most accurate endpoint temperature prediction, and the \(k\)-NN model proved to have the most accurate carbon prediction. Unfortunately, MARS models failed in training from combined static and dynamic data. The MARS failed due to the higher variability of inputs and low correlation between inputs and targets. The modeling and prediction of BOS from static data investigated how the performance of individual machine learning methods changes after adding lime and dolomitic lime as additional input observations. The results showed that the SVR models improved their performance index in testing in the case of temperature prediction. Although other models reduced their prediction performance in testing, the piecewise-cubic MARS model remained the most powerful. In testing carbon prediction, it improved the performance of the piecewise-linear MARS model, the SVR model with a Gaussian kernel, and NN. However, other models in the test phase decreased in prediction performance. Therefore, each machine learning method must select the optimal input parameters. Regarding the quality of dynamic temperature prediction, the SVR method with a polynomial kernel and the piecewise-cubic MARS model proved to be the most effective. The simulated temperature in these cases corresponded most closely to the standard temperature profile, as reported in the literature (e.g., [3; 4; 5; 45; 46]).