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.

翻译：本研究提出了一种基于机理解释的强化学习框架，用于翼型形状优化。通过采用双延迟深度确定性策略梯度算法（TD3）因其卓越的稳定性，我们的方法解决了流体动力学约束下形状优化的复杂性问题。采用基于偏微分方程（PDEs）的求解器以保证在探索过程中构型和几何形状发生极端变化时的精度。应用基于对偶加权残差的网格细化策略，确保目标泛函的精确计算。为简化迭代优化过程并处理几何变形，我们的方法整合了拉普拉斯平滑、自适应细化及贝塞尔曲线拟合策略。这一组合不仅能缓解网格缠绕问题，还能确保翼型几何的精确操控。我们的神经网络架构利用贝塞尔曲线进行高效降维，从而增强学习过程并保证翼型几何精度。网络中还嵌入了注意力机制以计算状态上的潜在动作。此外，针对翼型优化的特定挑战，我们引入了不同的奖励与惩罚机制。该算法旨在支持优化任务，为翼型形状优化提供更具针对性和有效性的方法。