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

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.