Machine Learning Prediction of Airfoil Aerodynamic Performance Using Neural Network Ensembles

Abstract

Featured Application: This research introduces a fast and reliable method for predicting aerodynamic performance using a deep learning approach, enabling efficient integration into preliminary design and optimization workflows. In addition, it presents a novel investigation into the influence of random seed selection, a factor that is virtually never addressed in aerodynamic machine learning studies, demonstrating its significant effect on model accuracy and reproducibility. Reliable aerodynamic performance estimation is essential for both preliminary design and optimization in various aeronautical applications. In this study, a hybrid deep learning model is proposed, combining convolutional neural networks (CNNs) and operating directly on raw airfoil geometry, with parallel branches of fully connected deep neural networks (DNNs) that process operational parameters and engineered features. The model is trained on an extensive database of NACA four-digit airfoils, covering angles of attack ranging from −5° to 14° and ten Reynolds numbers increasing in steps of 500,000 from 500,000 up to 5,000,000. As a novel contribution, this work investigates the impact of random seed initialization on model accuracy and reproducibility and introduces a seed-based ensemble strategy to enhance generalization. The best-performing single-seed model tested (seed 0) achieves a mean absolute percentage error (MAPE) of 1.1% with an (Formula presented.) of 0.9998 for the lift coefficient prediction and 0.57% with an (Formula presented.) of 0.9954 for the drag coefficient prediction. In comparison, the best ensemble model tested (seeds 610, 987, and 75025) achieves a lift coefficient MAPE of 1.43%, corresponding to (Formula presented.) 0.9999, and a drag coefficient MAPE of 1.19%, corresponding to (Formula presented.) = 0.9968. All the tested seed dependencies in this paper (ten single seeds and five ensembles) demonstrate an overall (Formula presented.) greater than 0.97, which reflects the model architecture’s strong foundation. The novelty of this study lies in the demonstration that the same machine learning model, trained on identical data and architecture, can exhibit up to 250% variation in prediction error solely due to differences in random seed selection. This finding highlights the often-overlooked impact of seed initialization on model performance and highlights the necessity of treating seed choice as an active design parameter in ML aerodynamic predictions.