## 7 Conclusions  
This study proposes an improved cement bond quality prediction method based on the Wide and Deep neural network. By incorporating the rheological characteristics of cement slurry and embedding the temperature-corrected equations for the consistency coefficient and flow behavior index into the network structure, the model can more accurately characterize the flow behavior of cement slurry under varying temperature and shear conditions, thereby significantly enhancing the prediction accuracy of cement bond quality. Experimental results show that the optimized Wide and Deep model outperforms traditional neural network models in terms of recall, precision, and F1-score. The overall accuracy reaches 87%, representing an improvement of approximately 4%, with a particularly notable enhancement of 6% in identifying Poor (low-quality bond) cases. Furthermore, the model was validated using real field data from the third-stage cementing section of an actual well. The predicted results were compared with acoustic amplitude logging evaluations, achieving a prediction accuracy of 89%, thus demonstrating excellent field applicability. To further investigate the impact of physical knowledge embedding on model training, two models with identical architectures were designed: one with embedded physical equations and the other using traditional weight-based computations. Gradient analysis during training revealed that the conventional model was prone to gradient vanishing, whereas the model with embedded physical equations achieved stable convergence while maintaining nonzero gradients. This ensured continuous weight updates and improved prediction accuracy. These findings explain, from a gradient perspective, how embedding physical knowledge enhances model performance. The Wide and Deep intelligent prediction approach proposed in this study provides an efficient and accurate decision-support tool for cement bond quality evaluation. It can also be applied to optimize cementing parameters and reduce operational risks, offering both theoretical foundation and practical guidance for the advancement of intelligent cementing technologies. Conceptualization, R.L. and J.Y. ; methodology, J.Y. ; software, L.L. ; validation, L.L. ; writing--review and editing, Z.W. ; formal analysis, Z.W. ; investigation, S.Z. ; investigation, S.Z. ; data curation, S.Z. ; resources, Z.Z. ; data curation, Z.Z. ; writing--original draft preparation, R.L. ; writing--review and editing, R.L. ; visualization, R.L. ; supervision, R.L. ; project administration, J.Y. ; funding acquisition, R.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the Joint Funds of the National Natural Science Foundation of China (Grant No. U22B6003). This study does not involve humans or animals. Therefore, the Institutional Review Board Statement is not applicable. This study does not involve human participants. Therefore, the informed consent statement is not applicable. The authors do not have permission to share data. Author [PERSON], [PERSON] and [PERSON] were employed by the company SINOPEC Research Institute of Petroleum Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The rheological calculation results of cement slurry for the remaining wells in this study are shown in the figures. From Figure 11, it can be seen that the cement slurry applied in this study conforms to the power-law model. Moreover, the fitting performance of the model improves after temperature correction.