The world steel industry is highly dependent on the use of electric arc furnaces (EAFs). The application of the electric arc phenomenon causes many power quality (PQ) problems, such as harmonics or voltage flickering. An adequate EAF model is useful for the design and control of EAFs and PQ improvement systems. In this paper, we propose an approach to EAF modeling based on a deterministic differential equation that is enhanced with stochastic ingredients. The identification of time series that represent equation coefficients is carried out using a genetic algorithm. The final solution includes two models of the electric arc furnace, both based on long short-term memory (LSTM) networks. They recreate the time series of the coefficients with given stochastic properties. The first model uses LSTM to generate the main component of the output signal, while the second applies LSTM to include the high frequency component. The potential of LSTM models to reflect different stages of the EAF work cycle, that is, the melting and refining stages, has been investigated. The results indicate that the LTSM model outperforms chaotic or stochastic models in both stages considered.