Inverse design approach, which directly generates optimal aerodynamic shape with neural network models to meet designated performance targets, has drawn enormous attention. However, the current state-of-the-art inverse design approach for airfoils, which is based on generative adversarial network, demonstrates insufficient precision in its generating and training processes and struggles to reveal the coupling relationship among specified performance indicators. To address these issues, the airfoil inverse design framework based on the classifier-free guided denoising diffusion probabilistic model (CDDPM) is proposed innovatively in this paper. First, the CDDPM can effectively capture the correlations among specific performance indicators and, by adjusting the classifier-free guide coefficient, generate corresponding upper and lower surface pressure coefficient distributions based on designated pressure features. These distributions are then accurately translated into airfoil geometries through a mapping model. Experimental results using classical transonic airfoils as examples show that the inverse design based on CDDPM can generate a variety of pressure coefficient distributions, which enriches the diversity of design results. Compared with current state-of-the-art Wasserstein generative adversarial network methods, CDDPM achieves a 33.6% precision improvement in airfoil generating tasks. Moreover, a practical method to readjust each performance indicator value is proposed based on global optimization algorithm in conjunction with active learning strategy, aiming to provide rational value combination of performance indicators for the inverse design framework. This work is not only suitable for the airfoils design, but also has the capability to apply to optimization process of general product parts targeting selected performance indicators.

翻译：逆设计方法通过神经网络模型直接生成满足指定性能目标的最优气动外形，已引起广泛关注。然而，当前基于生成对抗网络的翼型逆设计方法在生成和训练过程中精度不足，且难以揭示指定性能指标间的耦合关系。为解决这些问题，本文创新性地提出了基于无分类器引导去噪扩散概率模型（CDDPM）的翼型逆设计框架。首先，CDDPM能够有效捕捉特定性能指标间的关联性，并通过调整无分类器引导系数，基于指定的压力特征生成相应的上下表面压力系数分布。随后通过映射模型将这些分布精确转化为翼型几何形状。以经典跨音速翼型为例的实验结果表明，基于CDDPM的逆设计能够生成多样化的压力系数分布，从而丰富了设计结果的多样性。与当前最先进的Wasserstein生成对抗网络方法相比，CDDPM在翼型生成任务中实现了33.6%的精度提升。此外，本文基于全局优化算法结合主动学习策略，提出了一种重新调整各性能指标值的实用方法，旨在为逆设计框架提供合理的性能指标值组合。本工作不仅适用于翼型设计，还能够应用于针对选定性能指标的通用产品部件优化过程。