A Generative Approach To Transonic Wing Pressure Prediction

  • Francés-Belda, Víctor (INTA)
  • Sanmiguel Vila, Carlos (INTA)
  • Castellanos, Rodrigo (UC3M)

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Diffusion based generative models have recently emerged as a powerful alternative to conventional regression and autoencoding strategies because they learn full conditional data distributions rather than only conditional averages. This is particularly important for transonic aerodynamic fields, where shock waves induce highly non-linear and non-Gaussian behaviour that deterministic regressors tend to smooth out. Motivated by this, we introduce a surrogate modelling framework for predicting aerodynamic pressure coefficient (Cp) fields over aircraft wings using conditional Denoising Diffusion Probabilistic Models (DDPMs). The approach combines reduced order modelling and generative learning to approximate high dimensional Reynolds Averaged Navier Stokes solutions under varying flight conditions. Principal Component Analysis (PCA) is first used to compress the Cp fields into a low dimensional latent space, on which a conditional DDPM is trained to learn a stochastic reverse diffusion process conditioned on the flight parameters. Unlike autoencoder-based regressors, which converge to conditional means and therefore produce blurred reconstructions, the diffusion model preserves the sharp pressure gradients and discontinuities associated with transonic shock systems. The method is assessed on an open-source database of steady aerodynamic cases based on the NASA Common Research Model, covering transonic flow regimes characterised by strong non-linearities and shock-wave phenomena. In addition to the standard noise-prediction objective, a modified signal-space loss formulation is introduced, which directly optimises reconstruction fidelity of the aerodynamic fields. Comparisons against a baseline PCA-based autoencoder coupled with Gaussian process regression demonstrate a substantial reduction in global prediction error, alongside improved robustness in capturing shock-induced pressure gradients. These results indicate that conditional DDPMs constitute a promising alternative to traditional regression-based surrogates for aerodynamic field prediction, offering enhanced expressiveness and generalisation capabilities for complex flow regimes.