## 2 Materials and Methods
### Artificial Neural Network Model  
To calculate the decarburization curves using Equation (2), it is necessary to know the final carbon concentration in the molten steel and the total amount of carbon oxides emitted during the entire operating period. Therefore, we cannot directly use Equation (2) to predict the real-time decarburization rate during operation. Instead, we built a predictive model that learns the decarburization curves for various operations using Artificial Neural Networks (ANNs).  
The ANN model consisted of an input layer with eight inputs, a hidden layer with five neurons and an output layer with one output (Figure 2). We used the main factors affecting the decarburization rate along with the carbon oxide concentrations in the off-gas as inputs to the model and used the output value of the decarburization curve as the target value. In Figure 2, the operation time is the time elapsed from the start of the operation until each datum is collected and the CO and CO\({}_{2}\) concentration means the sum of carbon oxides measured at each time point. One thing to mention is the added carbon weight. In some cases, operators may insert additional carbon into the molten steel during operation in order to achieve the target carbon concentration in consideration of the composition, temperature and operating time of the molten steel. Since the additional carbon directly affects the final carbon concentration, we used it as an input to the ANN model.  
The input variables can be categorized into four groups. The weight of molten steel, initial carbon content and added carbon weight decide the total amount of dissolved carbon content. The pressure in the vacuum chamber, circulation flow rate and TOB flow rate indicate the control parameters which affect the decarburization rate. The operating time is the main factor that has the greatest influence on the final dissolved carbon content, if other conditions are equal. The CO and CO\({}_{2}\) concentrations are the indicators which show the current decarburization rate.  
All the features were min-max normalized. For simplicity, we assumed that the concentration of CO and CO\({}_{2}\) was between 0 and 100% and the pressure in the vacuum chamber was between 0 and 101.3 kPa. We used the actual maximum and minimum values for the other variables for the normalization.  
From March 2016 to December 2017, we obtained a total of 626 operation data from the 300 ton-RH process of POSCO Gwangyang Works, of which 70% was used as training data and the remaining 30% was used as test data. The data can be divided into three groups according to when the data were collected; the second quarter of 2016 (Period 1), the first quarter of 2017 (Period 2) and the fourth quarter of 2017 (Period 3).  
Figure 2: Input and output parameters of the ANN model. The target carbon contents are the result of the decarburization curve. The unit of the carbon content is parts per million (ppm), which means the weight fraction of carbon in molten steel.  
In the model, the activation function of the hidden layer was Rectified Linear Unit (ReLU) and that of the output layer was a linear function. To train the model, we used Adaptive Moment Estimation (Adam) as an optimizer and Mean Squared Error (MSE) as a loss function. To obtain a generalized model, we trained the model using 10-fold cross validation. We tested some combination of the number of hidden layers and the number of neurons in each layer. The number of hidden layers was set to 1, 2 or 3 and the number of neurons in each hidden layer was changed to 5, 10 and 15. The performance of the models was compared using the Root Mean Squared Error (RMSE) values of the validation data for all 39 cases.