## 6 Conclusions  
This study has evaluated the effectiveness of six supervised ML models in predicting the thermal conductivity of EG-Al2O3 nanofluids. A total of 94 experimental data points sourced from four published studies were used to train and test these models. These models were assessed using several performance indices. Additionally, regression analysis and a Taylor diagram were utilized to visually summarize the model performance. The model validation was conducted by re-predicting a subset of each experimental study. Furthermore, SHAP analysis was employed to interpret the models and identify the importance of each feature in the predictions as well as their contribution to the prediction. The main conclusions are as follows:  
1. The results of the model evaluation indicated that the GBDT model achieved the most satisfactory performance among the six models. In particular, the performance indices obtained by the GBDT model using the training and test sets are both acceptable: MSE of 6.7735 \(\times\) 10\({}^{-6}\) and 1.0859 \(\times\) 10\({}^{-5}\), RMSE of 0.0026 and 0.0033, MAE of 0.0009 and 0.0028, R\({}^{2}\) of 0.9974 and 0.9958, and MAPE of 0.2764% and 0.9695%. 2. The sensitivity analysis using SHAP values revealed that T had the highest impact on model prediction, with the highest importance value of 0.16 among all features. The feature importance ranking was determined as T > VF > D. The dependence plots further illustrate that T had a positive contribution to thermal conductivity. In addition, VF had a globally positive contribution to thermal conductivity, but D generally had a negative contribution to thermal conductivity, except under specific conditions such as D values of 13 nm, 43 nm, and 50 nm with a volume fraction of 0.1%. In summary, the GBDT model proved to be the most effective in predicting the thermal conductivity of EG-Al2O3 nanofluids, demonstrating the potential of ML models to outper  
Figure 14: (**a–c**) SHAP dependence plots of T, VF, and D based on the optimal model. form traditional theoretical models and numerical simulations. The use of ML models can significantly aid in the development and optimization of thermal management applications. However, a limitation of this study is that all data were sourced from existing literature, which may affect the models' generalization capability. Future research should focus on collecting more experimental data to enhance the models' robustness and generalizability. Additionally, exploring more metaheuristic algorithms could further improve the accuracy and reliability of the proposed models. Conceptualization, [PERSON] and C.L. ; methodology, T.Z. ; software, T.Z. ; validation, T.Z., X.M., J.Z. and C.L. ; formal analysis, T.Z. and X.M. ; investigation, T.Z. and X.M. ; resources, T.Z. and J.Z. ; data curation, T.Z. and J.Z. ; writing--original draft preparation, T.Z. ; writing--review and editing, X.M., J.Z. and C.L. ; visualization, T.Z. and X.M. ; supervision, J.Z. and C.L. ; project administration, J.Z. and C.L. ; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the China Scholarship Council (Grant No. 202106370038). Not applicable. The data used in this study are from published research: [PERSON] et al. (2014) ([[https://doi.org/10.1186/1556-276X-6-221](https://doi.org/10.1186/1556-276X-6-221)]([https://doi.org/10.1186/1556-276X-6-221](https://doi.org/10.1186/1556-276X-6-221)), accessed on 1 May 2024), [PERSON] et al. (2014) ([[https://doi.org/10.1007/s11051-009-9716-9](https://doi.org/10.1007/s11051-009-9716-9)]([https://doi.org/10.1007/s11051-009-9716-9](https://doi.org/10.1007/s11051-009-9716-9)), accessed on 1 May 2024), [PERSON] et al. (2014) ([[https://doi.org/10.1007/s11051-008-9500-2](https://doi.org/10.1007/s11051-008-9500-2)]([https://doi.org/10.1007/s11051-008-9500-2](https://doi.org/10.1007/s11051-008-9500-2)), accessed on 1 May 2024), and [PERSON] et al.