## 6 Conclusions  
This study improves cost contingency estimation for infrastructure projects by incorporating project-specific characteristics and a complexity index into both point and interval estimates. Among the seven ML algorithms tested, the ANN stood out as having the highest predictive accuracy for point estimates, achieving an \(R^{2}\) of 0.808. The inclusion of a complexity index constructed from cost and duration data significantly improved the ANN's performance, increasing its \(R^{2}\) to 0.899 from 0.808. For interval estimates, bootstrapping more accurately represented uncertainty, while Monte Carlo dropout produced narrower prediction intervals. The complexity index notably boosted interval prediction performance, improving the uncertainty accuracy by 27% in Monte Carlo dropout and 10% in bootstrapping.  
Theoretically, this study advances cost contingency estimation techniques by applying ML to project cost management and comparing multiple algorithms' performance. Ithighlights the importance of including a complexity index, especially in highly complex infrastructure projects, and extends contingency prediction to interval estimates. These improvements help provide a deeper understanding of project cost risks and offer project managers valuable confidence ranges to better manage cost uncertainties.  
Practically, practitioners can leverage the novel ANN-based model to enhance infrastructure cost planning and improve project delivery. The high predictive accuracy of ANNs positions them as a viable tool for practitioners conducting cost contingency estimations. Refined interval predictions equip project managers with better foresight into potential cost variances, enabling proactive cost management. For a new infrastructure project, key parameters such as project type, PEs, approved PEs, contract contingency, and planned duration can be readily obtained. Using these features, practitioners can quickly and accurately estimate a reasonable cost contingency, streamlining decision-making and reducing budget uncertainties. In summary, the ANN-based model offers a robust and efficient approach to cost estimation, equipping industry professionals with data-driven insights to enhance cost resilience and infrastructure project performance.  
This study's limitations include using a small dataset, which may restrict the generalizability of the results. A more extensive dataset could improve the model's applicability across diverse project scenarios, as its predictive performance may vary in different contexts or larger-scale infrastructure developments. Future research could address this by using larger datasets to further validate the complexity index and enhance its robustness. In addition, the models used only six input variables due to data limitations. Future studies could improve the accuracy and robustness of their results by incorporating more variables. Moreover, cost contingency values were derived indirectly rather than from direct project records; future research should utilize actual cost contingency data to improve validity. Finally, the study focuses on infrastructure projects within a single geographical region, i.e., Hong Kong. Future research should explore the model's performance in different geographical contexts to assess its broader applicability.  
Conceptualization, M.C.P.S. and Q.M.; Data curation, M.C.P.S.; Formal analysis, Q.M.; Methodology, M.C.P.S., Q.M. and Q.G.; Validation, Q.G.; Writing--original draft, Q.M.; Writing--review and editing, M.C.P.S. and Q.G. All authors have read and agreed to the published version of the manuscript.  
The research is supported by the PolyU BRE incentive scheme P0047727.  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
The authors would like to thank the Development Bureau of the HKSAR for sharing real-life project records for this study.  
The authors declare no conflicts of interest.