Engineering design methods aim to generate new designs that meet desired performance requirements. Past work has directly introduced conditional Generative Adversarial Networks (cGANs) into this field and achieved promising results in single-point design problems(one performance requirement under one working condition). However, these methods assume that the performance requirements are distributed in categorical space, which is not reasonable in these scenarios. Although Continuous conditional GANs (CcGANs) introduce Vicinal Risk Minimization (VRM) to reduce the performance loss caused by this assumption, they still face the following challenges: 1) CcGANs can not handle multi-point design problems (multiple performance requirements under multiple working conditions). 2) Their training process is time-consuming due to the high computational complexity of the vicinal loss. To address these issues, A Continuous conditional Diffusion Probabilistic Model (CcDPM) is proposed, which the first time introduces the diffusion model into the engineering design area and VRM into the diffusion model. CcDPM adopts a novel sampling method called multi-point design sampling to deal with multi-point design problems. Moreover, the k-d tree is used in the training process of CcDPM to shorten the calculation time of vicinal loss and speed up the training process by 2-300 times in our experiments. Experiments on a synthetic problem and three real-world design problems demonstrate that CcDPM outperforms the state-of-the-art GAN models.

Recently, extensive studies have focused on analyzing aerodynamic performance due to its important impact on aircraft design. Most of these works compute the aerodynamic coefficient of the airfoil through computational fluid dynamics (CFD) simulation, which is too time-consuming. To reduce the computational time required, some intelligence-based methods have been presented. However, these methods also suffer from certain issues. First, most of them directly implement existing machine learning methods used to predict the aerodynamic coefficient without adding any improvements. Second, some methods convert the airfoil shape and aerodynamic curves into images, which may lead to curve distortion and the introduction of noise. Third, some methods learn the relationship between the airfoil shape and aerodynamic coefficients but ignore the influence of initial inflow conditions. Accordingly, to address these issues, we propose an intelligent method for predicting the pressure coefficients (Cp) of airfoil based on a conditional generative adversarial network (cGAN). More specifically, we first present a two-step data augmentation strategy designed to expand the original airfoil dataset. Subsequently, we design a novel cGAN-based neural network to predict the Cp curve. To the best of our knowledge, this is the first work to apply generative adversarial network (GAN) to aerodynamic coefficient prediction. Moreover, we design a new loss function to train our network. Extensive experimental results demonstrate that the Cp curve predicted by our method is very close to that generated via CFD simulation. More importantly, our method achieves a speedup close to 1000x compared with CFD simulation.