Accelerating adjoint-based aerodynamic shape optimization through integrating reduced-order modeling and active learning

Owing to its computational efficiency in gradient evaluation, the adjoint method has emerged as a cornerstone in the field of aerodynamic shape optimization. However, the efficiency of the adjoint-based aerodynamic shape optimization relies on the cost of solving adjoint equations, which still remains time-consuming. In this paper, the adjoint method is accelerated by constructing efficient dynamic Reduced-Order Models (ROMs) enhanced by the active learning strategy. During each adjoint optimization step, the query function, i.e., also the objective function, is introduced to obtain relevant additional samples for updating the dynamic ROM. The updated ROM then predicts an improved initial guess for the adjoint solver, enabling faster convergence and accelerating the overall optimization process. The proposed Active Learning ADjoint (ALAD) method does not require additional simulation for model update, and is easy to combine with other acceleration methods. The efficiency of the proposed method is verified by airfoil shape optimization in both transonic inviscid and subsonic laminar flow regimes. Results indicate that the proposed ROM significantly reduces the initial residual of pseudo-time iterations, thus significantly decreasing the iteration numbers required by adjoint optimization. Finally, we combine ALAD with the dynamic mode decomposition (DMD) acceleration method, showing that this approach can be combined with other methods to further enhance the optimization efficiency. The proposed method holds great promise for a wide range of applications in aerospace engineering.