Next-Gen Models for Aero: Diffusion, Transformers, and Flow Matching
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Denoising diffusion probabilistic models (DDPMs) have emerged as a powerful approach for data generation. These models have become particularly popular in image generation and form the backbone of many of today’s state-of-the-art image generators. Flow matching is a more recent paradigm that is closely related to diffusion models; however, instead of learning how to remove noise, it learns probability paths that transform a well-known distribution, such as a Gaussian, into an unknown data distribution, thereby enabling data generation. Flow matching underpins several state-of-the-art generative models, including Stable Diffusion 3, Flux 2, and Sora 2. In this work, we adapt these frameworks to train generative models on computational fluid dynamics (CFD) data rather than images. Specifically, we use the pressure coefficient (Cp) distribution over an airfoil for different Mach numbers and angles of attack. In image generation tasks, models are typically conditioned on natural language inputs (commonly referred to as prompts) to control the generated outputs. In our approach, we replace this conditioning mechanism with a high-dimensional projection of the Mach number and angle of attack. This allows us to control the generation of new Cp distributions according to the desired physical conditions. We also investigate different neural network architectures, including U-NETs which are based on convolutions and were used in the earliest diffusion implementations, and Diffusion Transformers (DiTs), which are based on Vision Transformers and appear to scale more effectively than U-NETs. Finally, we compare our approach with traditional machine learning models such as multilayer perceptrons (MLPs). The results show that our models, particularly those trained using flow matching, achieve superior accuracy.
