<p>Currently, utilizing deep learning techniques for flow field prediction has become an important research area. Existing deep learning-based flow field prediction models primarily focus on low-speed flow fields, while research on prediction methods for high-speed flow fields remains relatively scarce. However, predicting high-speed flow fields is crucial for the design and optimization of high-speed aircraft. Therefore, in this work, the vanilla deep operator network (DeepONet) and the Fusion DeepONet, a type of deep neural operator, are employed to predict high-speed flow fields. First, design parameters were sampled, and the open-source software OpenFOAM was used to obtain a dataset of axisymmetric curved shock wave flow fields. The selected design parameters consist of geometric parameters and flow conditions. Keeping the settings of the vanilla DeepONet and Fusion DeepONet identical, a detailed comparative analysis of the prediction accuracy of the two frameworks and their ability to capture curved shock waves was conducted. The results demonstrate that for the prediction of axisymmetric curved shock wave flow fields, the Fusion DeepONet significantly outperforms the vanilla DeepONet in both the prediction accuracy for the overall flow field and the precision of capturing curved shock waves. Additionally, in terms of the generalization (or extrapolation) capability beyond the training parameter space, the Fusion DeepONet also far surpasses the vanilla DeepONet. To gain deeper insights into the Fusion DeepONet framework, we investigated the impact of the levels of information fusion on the model performance and performed an analysis of the model using singular value decomposition. In conclusion, this study confirms the effectiveness of the Fusion DeepONet, a deep neural operator model, in predicting axisymmetric curved shock wave flow fields. It meets the requirements for the design and optimization of high-speed aircraft and holds significant engineering application value.</p>