  In this paper, a novel mechanism-driven reinforcement learning framework is
proposed for airfoil shape optimization. To validate the framework, a reward
function is designed and analyzed, from which the equivalence between the
maximizing the cumulative reward and achieving the optimization objectives is
guaranteed theoretically. To establish a quality exploration, and to obtain an
accurate reward from the environment, an efficient solver for steady Euler
equations is employed in the reinforcement learning method. The solver utilizes
the B\'ezier curve to describe the shape of the airfoil, and a Newton-geometric
multigrid method for the solution. In particular, a dual-weighted
residual-based h-adaptive method is used for efficient calculation of target
functional. To effectively streamline the airfoil shape during the deformation
process, we introduce the Laplacian smoothing, and propose a B\'ezier fitting
strategy, which not only remits mesh tangling but also guarantees a precise
manipulation of the geometry. In addition, a neural network architecture is
designed based on an attention mechanism to make the learning process more
sensitive to the minor change of the airfoil geometry. Numerical experiments
demonstrate that our framework can handle the optimization problem with
hundreds of design variables. It is worth mentioning that, prior to this work,
there are limited works combining such high-fidelity partial differential
equatons framework with advanced reinforcement learning algorithms for design
problems with such high dimensionality.
