## 5 Conclusions  
This study examined the effects of single and combined factors on the performance of ultra-high-performance concrete (UHPC) through experimental data. These innovations effectively addressed the limitations of previous studies, such as predicting concrete performance using different machine learning and deep learning methods. By conducting independent and combined analyses of these factors, the study provided a comprehensive understanding of their roles and complex, nonlinear interactions. The study produced the following results:  
1. By fine-tuning data processing and algorithm optimization, a three-dimensional graph was used to visually display the impact of each influencing factor on the compressive strength of UHPC. This method made it possible to optimize the material ratio in UHPC structures and construction, thereby achieving the expected performance targets in actual engineering projects. 2. The AOA-SVR hybrid model achieved the highest prediction accuracy (R\({}^{2}\) = 0.9628) compared to the ANNs, SVM, and SVR single models, with very low RMSE (1.5779 MPa) and MAE (1.1796 MPa) values on both the training and test sets, indicating that the model did not suffer from overfitting. 3. Based on the SHAP impact summary and feature importance analysis, the AOA-SVR hybrid model showed that the cement content had the greatest impact on the compressive strength of UHPC, while the impact of slag powder was the smallest. In terms of model construction, this study developed a hybrid model by combining the whale optimization algorithm (AOA) and support vector regression (SVR) to overcome the limitations of single models in handling multi-factor, nonlinear problems. The successful application of this hybrid model indicates that further research can explore the combination of other optimization algorithms, such as particle swarm optimization algorithm and genetic algorithm, with SVR or other machine learning models to further improve prediction accuracy. Future research directions can include the following:  
1. The scope of the data set can be further expanded to cover more UHPC mix ratios and external environmental conditions to verify the generalizability of the model. 2. It is advisable to incorporate additional influencing factors--such as environmental humidity and temperature--in the construction of a more comprehensive prediction model. 3. Future research might well concentrate on the development of intelligent systems designed for real-time monitoring and prediction of UHPC performance, thereby enabling dynamic adjustments of material ratios. To enhance the provided paragraph and add the necessary details for applying the heatmap method to other material science fields, here is a Python program for creating a heatmap. This example will guide you through the steps to visualize the correlation matrix for different input variables and their relationships, which can be used for predicting material properties such as compressive strength. **Author Contributions:** Conceptualization, L.W. and D.D. ; methodology, L.W., L.L. and D.D. ; software, L.W., B.L. and Z.C. ; validation, L.W., L.L., D.D., B.L. and Z.C. ; investigation, L.L. and D.D. ; data curation, D.D. ; writing--original draft preparation, L.L., L.W., D.D., B.L. and Z.C. ; writing--review and editing, L.W. and B.L. ; visualization, L.W. ; supervision, L.W. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 12102269), the General Fund of Liaoning Provincial Science and Technology Fund (Grant No. 2022-MS-402), and the Shenyang Key Laboratory of Safety Evaluation and Disaster Prevention of Engineering Structures (Grant No. S230184). **Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study. **Data Availability Statement:** The original contributions presented in this study are included in the article, and further inquiries can be directed to the corresponding author.