Aircraft manufacturing is the jewel in the crown of industry, among which generating high-fidelity airfoil geometries with controllable and editable representations remains a fundamental challenge. While existing deep-learning-based methods rely on predefined parametric function families, e.g., B\'ezier curves and discrete point-based representations, they suffer from inherent trade-offs between expressiveness and resolution flexibility. To tackle this challenge, we introduce FuncGenFoil, a novel function-space generative model that directly learns functional airfoil geometries. Our method inherits both the advantages of arbitrary resolution sampling and the smoothness of parametric functions, as well as the strong expressiveness of discrete point-based functions. Empirical evaluations on the AFBench dataset demonstrate that FuncGenFoil improves upon state-of-the-art methods in airfoil generation by achieving a relative -74.4 label error reduction and +23.2 diversity increase on the AF-200K dataset. Our results highlight the advantages of function-space modeling for aerodynamic shape optimization, offering a powerful and flexible framework for high-fidelity airfoil design. Our code will be released.

We showcase the plain diffusion models with Transformers are effective predictors of fluid dynamics under various working conditions, e.g., Darcy flow and high Reynolds number. Unlike traditional fluid dynamical solvers that depend on complex architectures to extract intricate correlations and learn underlying physical states, our approach formulates the prediction of flow dynamics as the image translation problem and accordingly leverage the plain diffusion model to tackle the problem. This reduction in model design complexity does not compromise its ability to capture complex physical states and geometric features of fluid dynamical equations, leading to high-precision solutions. In preliminary tests on various fluid-related benchmarks, our DiffFluid achieves consistent state-of-the-art performance, particularly in solving the Navier-Stokes equations in fluid dynamics, with a relative precision improvement of +44.8%. In addition, we achieved relative improvements of +14.0% and +11.3% in the Darcy flow equation and the airfoil problem with Euler's equation, respectively. Code will be released at https://github.com/DongyuLUO/DiffFluid upon acceptance.

Transonic buffet is a flow instability phenomenon that arises from the interaction between the shock wave and the separated boundary layer. This flow phenomenon is considered to be highly detrimental during flight and poses a significant risk to the structural strength and fatigue life of aircraft. Up to now, there has been a lack of an accurate, efficient, and intuitive metric to predict buffet and impose a feasible constraint on aerodynamic design. In this paper, a Physics-Assisted Variational Autoencoder (PAVAE) is proposed to identify dominant features of transonic buffet, which combines unsupervised reduced-order modeling with additional physical information embedded via a buffet classifier. Specifically, four models with various weights adjusting the contribution of the classifier are trained, so as to investigate the impact of buffet information on the latent space. Statistical results reveal that buffet state can be determined exactly with just one latent space when a proper weight of classifier is chosen. The dominant latent space further reveals a strong relevance with the key flow features located in the boundary layers downstream of shock. Based on this identification, the displacement thickness at 80% chordwise location is proposed as a metric for buffet prediction. This metric achieves an accuracy of 98.5% in buffet state classification, which is more reliable than the existing separation metric used in design. The proposed method integrates the benefits of feature extraction, flow reconstruction, and buffet prediction into a unified framework, demonstrating its potential in low-dimensional representations of high-dimensional flow data and interpreting the "black box" neural network.

The modern aerodynamic optimization has a strong demand for parametric methods with high levels of intuitiveness, flexibility, and representative accuracy, which cannot be fully achieved through traditional airfoil parametric techniques. In this paper, two deep learning-based generative schemes are proposed to effectively capture the complexity of the design space while satisfying specific constraints. 1. Soft-constrained scheme: a Conditional Variational Autoencoder (CVAE)-based model to train geometric constraints as part of the network directly. 2. Hard-constrained scheme: a VAE-based model to generate diverse airfoils and an FFD-based technique to project the generated airfoils onto the given constraints. According to the statistical results, the reconstructed airfoils are both accurate and smooth, without any need for additional filters. The soft-constrained scheme generates airfoils that exhibit slight deviations from the expected geometric constraints, yet still converge to the reference airfoil in both geometry space and objective space with some degree of distribution bias. In contrast, the hard-constrained scheme produces airfoils with a wider range of geometric diversity while strictly adhering to the geometric constraints. The corresponding distribution in the objective space is also more diverse, with isotropic uniformity around the reference point and no significant bias. These proposed airfoil parametric methods can break through the boundaries of training data in the objective space, providing higher quality samples for random sampling and improving the efficiency of optimization design.

Aerodynamic performance evaluation is an important part of the aircraft aerodynamic design optimization process; however, traditional methods are costly and time-consuming. Despite the fact that various machine learning methods can achieve high accuracy, their application in engineering is still difficult due to their poor generalization performance and "black box" nature. In this paper, a knowledge-embedded meta learning model, which fully integrates data with the theoretical knowledge of the lift curve, is developed to obtain the lift coefficients of an arbitrary supercritical airfoil under various angle of attacks. In the proposed model, a primary network is responsible for representing the relationship between the lift and angle of attack, while the geometry information is encoded into a hyper network to predict the unknown parameters involved in the primary network. Specifically, three models with different architectures are trained to provide various interpretations. Compared to the ordinary neural network, our proposed model can exhibit better generalization capability with competitive prediction accuracy. Afterward, interpretable analysis is performed based on the Integrated Gradients and Saliency methods. Results show that the proposed model can tend to assess the influence of airfoil geometry to the physical characteristics. Furthermore, the exceptions and shortcomings caused by the proposed model are analysed and discussed in detail.