Arc models are crucial for predicting electric arcs’ behavior in circuit interruption scenarios, but traditional methods may inadequately capture the complexities of arc dynamics, prompting interest in advanced computational techniques for improved accuracy. To integrate the physical principles of arc models with black-box simulation methods, this paper presents an innovative simulation method that combines traditional Mayr and Cassie arc models with deep learning techniques. A dataset is generated using the one-dimensional Elenbaas-Heller equation to describe the arc model, and deep learning algorithms are integrated into the traditional arc model simulation. This results in a Black-box arc model simulation based on the DeepONet model. The feasibility of the proposed method is validated through experiments on two-phase short circuits in power system transmission lines. Compared to traditional methods, the deep learning-based Black-box approach demonstrates superior performance in terms of computational efficiency and accuracy.