# Machine Learning Prediction of Airfoil Aerodynamic Performance Using Neural Network Ensembles
## 5 Conclusions
From a practical engineering standpoint, the proposed framework can be readily integrated into early-stage aerodynamic design workflows. Potential applications include rapid airfoil screening for UAV conceptual design, optimization loops for low-speed aircraft, and preliminary performance estimation in parametric studies. This study presents a novel and highly relevant investigation within the field of machine learning for aerodynamic prediction, where both sensitivity and numerical precision are critical for evaluating model performance. Particular emphasis is placed on MAPE as a primary metric of predictive accuracy, which is especially important in aerodynamics due to the tight performance tolerances usually required in aerospace engineering applications. Nevertheless, the limitations of this present study stem primarily from the aerodynamic side, as the entire dataset is generated using XFOIL, a tool known to be less reliable in flow regimes involving separation or high angles of attack. This reliance on simulation-based data limits the real-world applicability of the results. From a machine learning perspective, although the proposed architecture has proven effective, it has not yet been extended to more complex three-dimensional cases. Additionally, ensemble modeling, while beneficial for accuracy, introduces increased computational costs, which may pose constraints in large-scale applications. The analysis in this paper highlights the critical role of random seed selection in ML-based aerodynamic prediction. Despite using an identical architecture and dataset, prediction errors vary substantially from overall MAPEs of 0.83% to 2.2%, depending solely on the choice of seed, whether single or ensemble. As shown in the values in Table 9, this results in an approximate 163% difference considering only the best/worst performing sets. However, as highlighted in Section 4, seeds can impact the performance of specific branches (lift or drag ML branches); therefore, this study identified cases in which fluctuation reaches 151.8% for \(C_{L}\) prediction and 359.65% for \(C_{D}\) prediction, summing up an overall MAPE fluctuation of 250%. Moreover, seeds are generally responsible for ensuring reproducibility in machine learning architectures; otherwise, each run of the same model will default to a randomly selected seed from the 32-bit integer space \(\left[0,2^{32}-1\right]\) available, leading to different results every time. In conclusion, controlling seed values is a necessary step in achieving the highest outcomes possible given a balanced ML architecture and a sized database. As such, evaluating multiple seeds, or using ensemble strategies, should be considered best practice in ML-based aerodynamic prediction workflows. Conceptualization, methodology, software, validation, formal analysis, investigation, data curation, writing--original draft preparation, writing--review and editing, D.-A.S.; visualization, supervision, writing--review and editing, L.-T.G., G.C., D.M. and C.-M.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. **Conflicts of Interest:** The authors declare no conflict of interest.