FuncGenFoil: Airfoil Generation and Editing Model in Function Space

TL;DR

FuncGenFoil introduces a function-space generative model for airfoils by combining flow matching with neural operators, enabling continuous, arbitrarily sampled airfoil curves and controllable editing. By modeling airfoils as functions and leveraging a GP prior along with a Fourier Neural Operator, the approach achieves state-of-the-art generation quality, increased design diversity, and precise editing capabilities, validated on multiple datasets and CFD simulations. The method demonstrates strong potential for aerodynamic shape optimization and high-fidelity manufacturing workflows, while acknowledging limitations in extending beyond airfoil-like geometries. Overall, it offers a flexible, resolution-agnostic framework that unifies parametric advantages with discrete-point expressiveness through function-space learning.

Abstract

Aircraft manufacturing is the jewel in the crown of industry, in which generating high-fidelity airfoil geometries with controllable and editable representations remains a fundamental challenge. Existing deep learning methods, which typically rely on predefined parametric representations (e.g., Bézier) or discrete point sets, face an inherent trade-off between expressive power and resolution adaptability. To tackle this challenge, we introduce FuncGenFoil, a novel function-space generative model that directly reconstructs airfoil geometries as function curves. Our method inherits the advantages of arbitrary-resolution sampling and smoothness from parametric functions, as well as the strong expressiveness of discrete point-based representations. Empirical evaluations demonstrate that FuncGenFoil improves upon state-of-the-art methods in airfoil generation, achieving a relative 74.4% reduction in label error and a 23.2% increase in diversity 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.

Figures (8)

• Figure 1: The conceptual difference between FuncGenFoil and previous airfoil representation methods. In many previous approaches, airfoils are represented either as parametric models, as shown in (a), or as discrete point-based models, as shown in (b). In contrast, (c) illustrates FuncGenFoil's approach, where an airfoil is treated as a continuous function mapped from a latent function, enabling a generative model in function space.
• Figure 2: Top: Overview of FuncGenFoil's neural network and training scheme. The model is a Fourier Neural Operator designed for point cloud data, although any other neural operator capable of general-purpose function-space approximation may be used. The model takes as input a function $u_t$ (point cloud data at an arbitrary resolution $d$), optional design condition variables $c$, and the generation time $t$. It then processes this input function consistently and outputs the current velocity operator $v_{\theta}(u_t, c, t)$ for calculating the flow matching loss. Bottom: Inference with FuncGenFoil is conducted by first sampling a random latent function from a Gaussian process and then reconstructing the airfoil by solving an ODE.
• Figure 3: Airfoil editing by FuncGenFoil. Given a original airfoil $u_1$, an editing requirement $\delta$ and target airfoil $u_1^{\delta}$. We first infer its latent function $u_0$ reversely, and make it learnable as $a_{\theta}$. Then we sample a new airfoil $u_1^{'}$, and conduct a regression in function space via maximum a posteriori estimation $\mathcal{L}_{\mathrm{MAP}}$. After a few iterations of fine-tuning, we can generate edited airfoil $u_1^{\delta}$ with high accuracy.
• Figure 4: Examples of eight different FuncGenFoil instances performing airfoil editing over 20 training iterations. The orange points and sections represent the editing requirements as constraints; the gray region is the original airfoil, while the blue region shows the generated edited airfoil. The results demonstrate that the generated airfoil quickly adapts to the editing requirements within a few iterations, achieving a natural and smooth function regression. The editing scheme can be completely customized according to the user's preference.
• Figure 5: Left: Comparison of the lift-to-drag ratio histograms for CRM wings in the original dataset and the samples generated by our FuncGenFoil model. Right: Visualization of the pressure coefficient for the generated CRM wings, obtained through aerodynamic simulation.