## 1 Introduction
In addition, they are often not suitable for real-time prediction due to inaccurate or excessive assumptions used in the model [15; 25]. Other researchers have studied data-driven modeling that combines real-time data collected from various sensors and machine learning algorithms. [PERSON] et al. [26; 27] use Fuzzy logic to predict the end point of decarburization in the middle of the RH operation. They have selected the main factors affecting the operating time through correlation analysis and multiple regression analysis and have constructed separate Fuzzy models according to the steel type. The prediction model learns the actual decarburization endpoint by the operator and does not account for changes in dissolved carbon content during operation. [PERSON] et al. [28; 29] propose a dynamic model of the RH process for online observation and model-based control. They calculate thermodynamic equilibrium and reaction kinetics by considering the cyclic process data and acyclic event data. The model shows excellent performance in predicting the decarburization rate as well as impurities and temperature changes of molten steel. However, there is a limit to obtaining a generalized model because the parameter identification of the physical model must be preceded. [PERSON] et al. [30] attempt to calculate the dissolved carbon content in real time during RH operations using the operator's experience, metallurgical knowledge and operational data. [PERSON] et al. [31] tried to predict the endpoint carbon content using the Radial Basis Function (RBF) neural network in a Vacuum Oxygen Decarburization (VOD) vacuum steel refining process. However, these studies show relatively large prediction errors due to the lack of consideration for the actual change in dissolved carbon content during operation. In addition to the RH process, the data-driven models are actively used in various fields of the steelmaking process and studies have been reported to predict the change of impurities [32; 33; 34] and temperature [35] of the molten steel. However, the difficulty of collecting dissolved carbon content data poses an obstacle to developing real-time prediction models in the RH process. In other words, it is not only difficult to measure the continuous change in the dissolvedcarbon during operation, but it is also time-consuming and expensive to obtain the actual carbon content under various operating conditions. In this work, we proposed a real-time prediction model for carbon content in molten steel using real-time operation data and the carbon oxide content in off-gas and showed that the decarburization end time could be accurately determined using the model. The main idea of this study is that carbon oxides emitted through the off-gas in the RH process come only from molten steel. If we know exactly the amount of carbon oxides in the off-gas at any given time, we can accurately infer the decarburization reaction rate at that time. However, the off-gas analyzer used in the general RH process is installed far from the vacuum chamber where the decarburization reaction takes place, so it is difficult to capture the decarburization reaction in the molten steel in time. So we firstly introduced a new type of gas analyzer, Tunable Diode Laser Absorption Spectroscopy (TDLAS), to the RH process and showed that the off-gas components emitted from the vacuum chamber could be measured faster and more accurately by using it. Next, we introduced a decarburization curve to estimate the carbon concentration in the molten steel using carbon monoxide and carbon dioxide concentrations in the off-gas measured by the TDLAS analyzer and confirmed the similarity between the results of the decarburization curve and the actual sampling data. Since the decarburization curve can be obtained after an operation is over, it cannot be used for online prediction. Instead, we used Artificial Neural Networks (ANNs) as an online prediction model for carbon content in the molten steel.