FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fields

TL;DR

FoilDiff introduces a diffusion-based surrogate for 2D airfoil flow fields that fuses a connected encoder–decoder with a latent transformer, enabling global context modelling and robust conditioning on geometry, Reynolds number, and angle of attack. By leveraging DDIM sampling and deep latent conditioning, FoilDiff achieves superior predictive accuracy and uncertainty calibration compared with state-of-the-art diffusion backbones, while maintaining practical inference speeds. The method demonstrates significant gains in both interpolation and extrapolation across diverse aerodynamic conditions, with substantial reductions in mean squared error and improved uncertainty metrics. The work highlights the potential of hybrid diffusion transformers for efficient, physics-aware aerodynamic surrogates and outlines future directions toward unsteady, three-dimensional flows and physics-informed extensions.

Abstract

The accurate prediction of flow fields around airfoils is crucial for aerodynamic design and optimisation. Computational Fluid Dynamics (CFD) models are effective but computationally expensive, thus inspiring the development of surrogate models to enable quicker predictions. These surrogate models can be based on deep learning architectures, such as Convolutional Neural Networks (CNNs), Graph Neural Networks (GNNs), and Diffusion Models (DMs). Diffusion models have shown significant promise in predicting complex flow fields. In this work, we propose FoilDiff, a diffusion-based surrogate model with a hybrid-backbone denoising network. This hybrid design combines the power of convolutional feature extraction and transformer-based global attention to generate more adaptable and accurate representations of flow structures. FoilDiff takes advantage of Denoising Diffusion Implicit Model (DDIM) sampling to optimise the efficiency of the sampling process at no additional cost to model generalisation. We used encoded representations of Reynolds number, angle of attack, and airfoil geometry to define the input space for generalisation across a wide range of aerodynamic conditions. When evaluated against state-of-the-art models, FoilDiff shows significant performance improvements, with mean prediction errors reducing by up to 85\% on the same datasets. The results have demonstrated that FoilDiff can provide both more accurate predictions and better-calibrated predictive uncertainty than existing diffusion-based models.

Figures (10)

• Figure 1: Graphical model of Denoising Diffusion Probabilistic Models
• Figure 2: Graphical model for non-Markovian inference models
• Figure 3: The FoilDiff architecture, incorporating an encoder, a latent transformer, and a decoder, with U-Net-style skip connections and deep latent embeddings to integrate conditional information effectively
• Figure 4: Latent transformer architectures. (a) Standard DiT architecture illustrating the conventional diffusion transformer pipeline peebles2023scalablediffusionmodelstransformers; (b) U-ViT architecture showing modifications bao2023worthwordsvitbackbone. $Z \in \mathbb{R}^{B \times M}$ denotes the latent representation obtained at the final block of the encoder, where $B$ is the batch size, $M$ the embedding dimension, and $D$ is the total number of blocks
• Figure 5: Structure of the dataset