Manifold Learning for Aerodynamic Shape Design Optimization

The significant computational cost incurred due to the iterative nature of Computational Fluid Dynamics (CFD) in traditional aerodynamic shape design frameworks poses a major challenge, especially in the context of modern integrated design requirements and increasingly complex design conditions. To address the demands of modern design, we developed an efficient aerodynamic shape design framework based on our previous work involving the locally linear embedding plus constrained optimization genetic algorithm (LLE+COGA) high-fidelity reduced-order model (ROM). An active manifold (AM) auto-en/decoder was employed to address the dimensionality curse arising from an excessively large design space. The fast mesh deformation method was utilized for high-precision, rapid mesh deformation, significantly reducing the computational cost associated with transferring geometric deformations to CFD fine mesh. This work addressed the transonic optimization problem of the undeflected Common Research Model (uCRM) three-dimensional wing (with an aspect ratio of 9), involving 241 design variables. The results demonstrate that the optimized design achieved a significant reduction in the drag coefficient by 38.9% and 54.5% compared to the baseline in Case 1 and Case 2, respectively. Additionally, the total optimization time was shortened by 62.6% and 57.7% in the two cases. Moreover, the optimization outcomes aligned well with those obtained from the FOM-based framework, further validating the effectiveness and practical applicability of the proposed approach.