## 1 Introduction
In recent years, some scholars have reconstructed similar heat transfer or mass transfer problems based on the rapidly developing deep learning algorithm, aiming to obtain a surrogate model that can consider the physical mechanism. [PERSON] et al. [19] adopted a convolutional neural network (CNN) to the prediction of the velocity field with different geometric shapes, while convolution and deconvolution operations were used to perform image-to-image regression. Although the accuracy rate reached 98%, there were prediction errors near the boundary. Based on the deep convolutional neural network, the \(Cp\)-\(u\) model was proposed by [PERSON] et al. [20] for the prediction of the unsteady velocity around a circular cylinder. Compared with the measured data, it had good accuracy. [PERSON] et al. [21] proposed an innovative framework based on the machine learning and CFD simulation to improve the prediction accuracy of turbine wake. The results of the turbine wake model based on ANN were in good agreement with the numerical and experimental data, which showed that the ANN can establish the complex spatial relationship of the problem. In summary, deep learning has been used in the reconstruction of problems such as velocity field, pressure field, and temperature field, and has shown high accuracy and performance. Based on the above introduction, it can be found that there are two main methods to predict the performance of components in power cycles, especially S-CO\({}_{2}\) turbines: the mechanism-based physical model and the data-based proxy model. The mechanism-based physical model is a conventional CFD solution method. It mainly solves NS equations on computational grids with corresponding boundary conditions. Although this method is accurate, the time and cost of calculation are very high. The performance prediction of related components shows high prediction efficiency and accuracy. However, it cannot capture the details of heat and mass transfer process in turbine. However, in solutions to similar problems, deep learning can overcome the above shortcomings. Therefore, in order to improve the accuracy and efficiency of performance prediction while preserving the physical field information, a performance prediction method of S-CO\({}_{2}\) turbines based on CNN is proposed. Our contributions are as follows:  
1. The performance of field reconstruction for an end-to-end deep learning method is explored in this research. The most existing machine learning methods only focus on one target variable in engineering design and optimization tasks. The fields predicted by our method can provide more flow mechanism explanations and help designers understand the physical process. 2. The data-based proxy model is established for a physical system. Traditional methods lack accuracy to some extent and require manual intervention. Based on the existing scientific database, this method does not need to rely on human intervention and has the advantages of being universal, flexible, and easy to implement, showing a good promise for real-time control and design optimization of turbines. 3. The method proposed in this research is effective and accurate. The off-design power and efficiency prediction in this method is able to reach performance comparable to a state-of-the-art model and clearly outperforms classical methods. In addition, once the deep model is well-trained, the calculation with GPU-accelerated can quickly predict the physical fields on the blade surface and turbine performance. This flexible and adaptive tool can not only reduce the design cycle of turbine components, but also help to grasp the actual operating conditions in real time, which can be applied to adjust and control the system in time. The rest of this paper is organized as below: Section 2 introduces the overall architecture of this research, the theory and method of CFD analysis and deep convolutional neural network; Section 3 is the results and discussion, including CFD off-design pre-analysis, flow field reconstruction, and performance prediction.