Comparative Study of Meta-Learning and Transfer Learning for the Prediction of Supercritical Airfoils Under Small-Scale Dataset

Machine learning has demonstrated significant potential as a valuable tool for aerodynamic design. However, collecting an abundant training set is usually computationally expensive and time-consuming. To address this data scarcity, meta-learning and transfer learning offer viable strategies. Meta-learning enables models to learn efficiently from limited data by leveraging experience across related tasks, while transfer learning reduces data requirements by reusing knowledge from pre-trained models. In addition, integrating physics knowledge into the models provides a complementary path to enhance the reliability and generalizability under data-scarce conditions. This paper studies meta-learning and transfer learning strategies to realize the prediction of supercritical airfoil pressure distribution under multiple free stream conditions with a small-scale dataset. All the models are tested both in the source domain and the target domain. Then, a systematic comparative analysis of different models across different target domain training sample scales is studied. Results show that meta-learning and transfer learning both improve target-domain performance compared to the baseline model. Yet, meta-learning still achieves limited accuracy in the target domain, and data-driven transfer learning exhibits poor generalization. Compared with data-driven models, the Mach number weighted transfer learning model provides more generalized results and higher accuracy.