*5.4. Prediction of the dc*/*dt for an Industrial Dataset*

We used a dataset that was acquired from an industrial reactor to evaluate the performance of our trained model. Figure 8 shows the comparison between the predicted values and the actual values of the dc/dt. Again, the authors would like to emphasize if the predicted value of the target as a function of the "true" values of the test samples follows the "y = x" line, one can conclude that the model performance is at its best. It is worth mentioning that we only used two features for this prediction: namely, total O2 flow and lance height. It is always one the goals of any machine-learning development to predict the target with a fewer number of variables/predictors. This is because if the model deals with many predictor variables, then there is a high chance that there are hidden relationships between some of them, leading to redundancy and, even if there is no relationship between any of them, the model can suffer from overfitting when there are a large number of predictor variables. In addition, a model that can predict with a fewer number of predictor variables is more practical due to some considerations, such as data availability, storage, computer resources, time taken for computation, etc. Thus, this is one of the achievements of this study, that the developed model can predict the target by only using two predictor variables.

The scatter plot demonstrates that our trained model could predict the dc/dt precisely. Figure 9 shows the error histogram for this prediction. The most frequent error was 0.000026. The metrics (Table 3, column 6) were recorded to be 0.25, 0.62, 0.04 and 0.009 for the mean absolute error, root mean squared error, relative absolute error and relative squared error, respectively. The coefficient of determination was computed to be 0.98. These values confirm that our trained model can be used at industries to predict and control the variation of the dc/dt in an actual reactor. Figure 8 shows that the machine-learning algorithm can predict the decarburization rate very accurately without employing any simplifications and without taking into account all the reactions, interactions, mass and heat transfers and fluid flows. In fact, all of these parameters are already inherited in the dataset, and an algorithm trained on the real dataset naturally learns the relationships between all of the parameters involved in the process without exactly knowing the physical meanings of them.

**Figure 8.** Scatter plot comparing the predicted values of the dc/dt using neural network method with the actual values of the dc/dt for an industrial dataset with the two operating parameters of total oxygen flow and lance height only.

**Figure 9.** Error histogram of the predicted values of the dc/dt for the industrial dataset with the two operating parameters of total oxygen flow and lance height only.
