Manifold-Preserving Guided Aerodynamic Modeling for Heterogeneous Data

Efficient and high-fidelity aerodynamic modeling can significantly accelerate the early-stage design process of aircraft. Recent studies have advanced aerodynamic modeling by utilizing high-dimensional heterogeneous data (such as surface pressure distribution) with autoencoders, achieving higher accuracy with fewer samples compared to traditional “end-to-end” approaches. This paper explores the mechanism behind this enhancement, exploiting manifold learning to extract valuable insights from high-dimensional data, thereby improving aerodynamic modeling accuracy. However, current research relies solely on a feature alignment in manifold space, which may introduce potential distortions and lead to modeling inaccuracies. To address this issue, we utilize a decoder model to constrain the latent space, which directly predicts high-dimensional pressure distributions from low-dimensional design or flight parameters, thereby preserving the manifold structure inherent in the original data. By integrating feature alignment with latent space constraint, we introduce a manifold-preserving aerodynamic modeling framework. A specially designed loss function operationalizes this approach, effectively capturing relevant information from high-dimensional pressure distributions. Transonic case studies involving two-dimensional airfoils and three-dimensional wings validate the superior modeling capabilities of the proposed method across different geometries and flow conditions. Additionally, visualizations are employed to compare this approach with existing aerodynamic modeling methods, further highlighting its advantages.