  Leveraging neural networks as surrogate models for turbulence simulation is a
topic of growing interest. At the same time, embodying the inherent uncertainty
of simulations in the predictions of surrogate models remains very challenging.
The present study makes a first attempt to use denoising diffusion
probabilistic models (DDPMs) to train an uncertainty-aware surrogate model for
turbulence simulations. Due to its prevalence, the simulation of flows around
airfoils with various shapes, Reynolds numbers, and angles of attack is chosen
as the learning objective. Our results show that DDPMs can successfully capture
the whole distribution of solutions and, as a consequence, accurately estimate
the uncertainty of the simulations. The performance of DDPMs is also compared
with varying baselines in the form of Bayesian neural networks and
heteroscedastic models. Experiments demonstrate that DDPMs outperform the other
methods regarding a variety of accuracy metrics. Besides, it offers the
advantage of providing access to the complete distributions of uncertainties
rather than providing a set of parameters. As such, it can yield realistic and
detailed samples from the distribution of solutions.
