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Leveraging neural networks as surrogate models for turbulence simulation is atopic of growing interest. At the same time, embodying the inherent uncertaintyof simulations in the predictions of surrogate models remains very challenging.The present study makes a first attempt to use denoising diffusionprobabilistic models (DDPMs) to train an uncertainty-aware surrogate model forturbulence simulations. Due to its prevalence, the simulation of flows aroundairfoils with various shapes, Reynolds numbers, and angles of attack is chosenas the learning objective. Our results show that DDPMs can successfully capturethe whole distribution of solutions and, as a consequence, accurately estimatethe uncertainty of the simulations. The performance of DDPMs is also comparedwith varying baselines in the form of Bayesian neural networks andheteroscedastic models. Experiments demonstrate that DDPMs outperform the othermethods regarding a variety of accuracy metrics. Besides, it offers theadvantage of providing access to the complete distributions of uncertaintiesrather than providing a set of parameters. As such, it can yield realistic anddetailed samples from the distribution of solutions. All source codes anddatasets utilized in this study are publicly available.

Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models