标题： 基于伴随的气动外形优化，带有由扩散模型学习的流形约束 显示英文标题

标题： Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models

摘要： 我们引入了一个基于伴随的气动外形优化框架，该框架整合了一个在现有设计上训练的扩散模型，以学习一个气动可行形状的平滑流形。 该流形被作为等式约束施加于外形优化问题。 我们方法的核心是计算设计目标（例如，阻力和升力）相对于流形空间的伴随梯度。 这些梯度首先通过对传统外形设计参数（例如，Hicks-Henne参数）计算外形导数，然后通过自动微分将它们反向传播到扩散模型的潜在空间中得到。 我们的框架保持了数学严谨性，并可以以最小的修改集成到现有的基于伴随的设计器流程中。 在使用现成的通用非线性优化器进行大量跨音速RANS翼型设计案例中进行了演示，我们的方法消除了随意的参数调整和变量缩放，保持了对初始化和优化器选择的鲁棒性，并相比传统方法实现了更优的气动性能。 这项工作阐明了AI生成的先验如何有效地与伴随方法结合，通过自动微分实现稳健、高保真的气动外形优化。 显示英文摘要

摘要： We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality constraint to the shape optimization problem. Central to our method is the computation of adjoint gradients of the design objectives (e.g., drag and lift) with respect to the manifold space. These gradients are derived by first computing shape derivatives with respect to conventional shape design parameters (e.g., Hicks-Henne parameters) and then backpropagating them through the diffusion model to its latent space via automatic differentiation. Our framework preserves mathematical rigor and can be integrated into existing adjoint-based design workflows with minimal modification. Demonstrated on extensive transonic RANS airfoil design cases using off-the-shelf and general-purpose nonlinear optimizers, our approach eliminates ad hoc parameter tuning and variable scaling, maintains robustness across initialization and optimizer choices, and achieves superior aerodynamic performance compared to conventional approaches. This work establishes how AI generated priors integrates effectively with adjoint methods to enable robust, high-fidelity aerodynamic shape optimization through automatic differentiation.