A mechanism-informed reinforcement learning framework for shape
  optimization of airfoils
Jingfeng Wang Guanghui Hu
In this study, we present the mechanism-informed reinforcement learning
framework for airfoil shape optimization. By leveraging the twin delayed deep
deterministic policy gradient algorithm for its notable stability, our approach
addresses the complexities of optimizing shapes governed by fluid dynamics. The
PDEs-based solver is adopted for its accuracy even when the configurations and
geometries are extraordinarily changed during the exploration. Dual-weighted
residual-based mesh refinement strategy is applied to ensure the accurate
calculation of target functionals. To streamline the iterative optimization
process and handle geometric deformations, our approach integrates Laplacian
smoothing, adaptive refinement, and a B\'ezier fitting strategy. This
combination not only remits mesh tangling but also guarantees a precise
manipulation of the airfoil geometry. Our neural network architecture leverages
B\'ezier curves for efficient dimensionality reduction, thereby enhancing the
learning process and ensuring the geometric accuracy of the airfoil shapes. An
attention mechanism is embedded within the network to calculate potential
action on the state as well. Furthermore, we have introduced different reward
and penalty mechanisms tailored to the specific challenges of airfoil
optimization. This algorithm is designed to support the optimization task,
facilitating a more targeted and effective approach for airfoil shape
optimization.