## 5 Conclusions  
This study primarily investigated the prediction of methane transcritical heat transfer coefficients under various channel shapes using machine learning approaches. Through a comprehensive analysis of data preprocessing, modeling outcomes of different models, feature selection results, and deep learning modeling performance, the following conclusions were drawn:  
(1) Different dataset division ratios significantly influence model performance. By comparing the ratios of 6:4, 7:3, and 8:2, it was found that the 7:3 ratio yielded the best performance in predicting heat transfer coefficients for both straight channels and hexagonal channels, achieving higher R\({}^{2}\) values and lower errors. (2) Among the modeling results of the different models, the artificial neural network (ANN) model performed outstandingly in both channel shapes, whether in full-feature modeling or after feature selection, demonstrating excellent R\({}^{2}\) and MAE values. (In the straight flow channel, R\({}^{2}\) is 0.882849; in the hexagonal flow channel, R\({}^{2}\) is 0.991593.) In contrast, other models such as random forest (RF), support vector machine (SVM), and XGBOOST were slightly inferior in prediction accuracy and fitting degree. (3) Among deep learning models, the LSTM and Transformer models demonstrated strong performance in predicting heat transfer coefficients for both channel types. Particularly, models incorporating attention mechanisms, such as LSTM-SE (achieving the highest R value of 0.938732 for the straight flow channel) and Transformer-LA (achieving the highest R\({}^{2}\) value of 0.999257 for the hexagonal flow channel), exhibited substantial performance improvements in both straight and hexagonal channels. This suggests that attention mechanisms can effectively enhance the model's capacity to capture key features, thereby improving prediction accuracy. **(4)** The SHAP analysis results indicated that the contributions of different channel types and sample features to model outputs vary significantly. In straight channels, features such as \"Dh\", \"RE\", and \"Qw\" have a greater impact on model outputs, while in hexagonal channels, features like \"Tinv\", \"Qw\", and \"PR\" are more important. Local explanation results further revealed that the importance of features varies among different samples, emphasizing the need to select the appropriate features for optimization based on the specific channel types and sample features in practical applications. In summary, this study proposes a data acquisition approach to obtain more extensive datasets; furthermore, we explore a variety of machine learning and deep learning models to validate the potential of deep learning models with attention mechanisms. Additionally, SHAP-based interpretable analysis offers valuable insights into understanding model predictions, thereby facilitating further model optimization and feature engineering. Meanwhile, this study highlights the primary direction for future research in this field, namely, integrating physical information with neural network models to achieve more accurate predictions of flow characteristics or exchange characteristics. The findings of this study provide a critical theoretical foundation and practical guidance for predicting methane transcritical heat transfer coefficients. Conceptualization, Y.S. and L.Z. ; methodology, Y.S., Y.Z. and L.Z. ; validation, Y.S. and L.Z. ; formal analysis, Y.S. ; investigation, Y.S. and J.W. ; data curation, Y.S., Y.Z. and J.W. ; writing--original draft preparation, Y.S. ; writing--review and editing, J.W. ; visualization, Y.S. and J.W. ; supervision, Y.Z. and L.Z. ; project administration, L.Z. ; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript. This research was supported by the major science and technology project of Hainan Province (ZDYF2023 GJS148). At the same time, We would like to express my sincere thanks to the professors who provided guidance for this research. Not applicable.