Airfoil Diffusion: Denoising Diffusion Model For Conditional Airfoil Generation

TL;DR

The paper tackles the challenge of generating high-performance airfoil geometries without relying on predefined parameterizations. It introduces a conditional denoising diffusion probabilistic model that operates directly in airfoil geometry space, trained on the UIUC dataset, and capable of generating new profiles from random vectors while conditioning on aerodynamic targets such as $C_l$ and $C_d$. By using NeuralFoil to rapidly estimate $C_l$ and $C_d$, the authors demonstrate both unconditional generation within the training space and conditional generation that achieves favorable lift-to-drag performance, with PCA confirming meaningful novelty within realistic design space. The approach expands the airfoil design space, enhances design efficiency, and enables rapid exploration of high-performance shapes, with future work including 3D extensions and multi-constraint conditioning.

Abstract

The design of aerodynamic shapes, such as airfoils, has traditionally required significant computational resources and relied on predefined design parameters, which limit the potential for novel shape synthesis. In this work, we introduce a data-driven methodology for airfoil generation using a diffusion model. Trained on a dataset of preexisting airfoils, our model can generate an arbitrary number of new airfoils from random vectors, which can be conditioned on specific aerodynamic performance metrics such as lift and drag, or geometric criteria. Our results demonstrate that the diffusion model effectively produces airfoil shapes with realistic aerodynamic properties, offering substantial improvements in efficiency, flexibility, and the potential for discovering innovative airfoil designs. This approach significantly expands the design space, facilitating the synthesis of high-performance aerodynamic shapes that transcend the limitations of traditional methods.

Figures (6)

• Figure 1: Overview of the Airfoil Diffusion Model: a) Airfoil conditioning information such as the coefficient of lift ($C_l$), coefficient of drag ($C_d$), maximum thickness, and maximum camber is passed through b) conditional embedding multi-layer perceptron (MLP) layers. The embedded conditioning information is passed to e) the denoising U-Net. During training, samples are progressively distorted to approximate Gaussian noise, as shown in c). In the inference phase, a noise vector d) along conditioning value embedding are input to the U-Net e), which outputs the conditionally generated airfoil profile in f).
• Figure 2: The conditioning input, such as $C_d$ or $C_l$ is fed through several multilayer perceptron layers to generate a context vector $z$ for conditioning the diffusion model. In the forward process, the sample y coordinates are subjected to noise for $T$ timesteps, gradually approaching gaussian noise. During the backward process, the model learns to estimate the added noise at each timestep $t$ given conditioning $z$ and $y_t$.
• Figure 3: Histograms of $C_l$, $C_d$, maximum camber, and maximum thickness for the UIUC (orange) and generated (blue) samples. The generated samples exhibit narrower distributions compared to the UIUC data, with their means slightly shifted to the left of the UIUC distributions.
• Figure 4: Scatter plots of the relationship between input conditioning values for $C_d$ and $C_l$ in (a) and (b), respectively. Also shown are the lines of best fit, along with the visual representation of the standard deviation from the line of best fit. In (b), the purple region depicts conditioning on values of $C_l$ seen in the training dataset, and the red region shows conditioning on values not seen in the UIUC dataset.
• Figure 5: a) Scatter plot of the $C_d$ (x-axis) and $C_l$ (y-axis) values from NeuralFoil evaluations for both the $C_d$-conditioned (blue points) and $C_l$-conditioned (green points) models. The $C_d$-conditioned model spans a broader range of $C_d$ values, while the $C_l$-conditioned model spans a broader range of $C_l$ values, with a bias towards lower $C_d$ values. b) Airfoils with the greatest lift-to-drag ratios from the $C_l$-conditioned model (green) and UIUC dataset (red). The top UIUC airfoils have elongated shapes with minimal thickness and varying degrees of camber, while the $C_l$-conditioned model generates airfoils that similarly exhibit reduced thickness and differing camber profiles. The $C_l$-conditioned airfoils generally achieve higher lift-to-drag ratios with slightly more thickness and less camber compared to the UIUC samples. c) Box plots of the lift-to-drag ratio for the $C_d$- and $C_l$-conditioned models and the UIUC dataset. The $C_l$-conditioned model exhibits a wider range of lift-to-drag ratios and produces samples with greater lift-to-drag ratios than those seen in the UIUC dataset.