Comparison of generative learning methods as turbulence surrogates

Abstract Numerical simulations of turbulent flows present significant challenges in fluid dynamics due to their complexity and high computational cost. High-resolution techniques such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are generally not computationally affordable, particularly for technologically relevant problems. Recent advances in machine learning, specifically in generative probabilistic models, offer promising alternatives as surrogates for turbulence. This paper investigates the application of three generative models — Variational Autoencoders (VAEs), Deep Convolutional Generative Adversarial Networks (DCGANs), and Denoising Diffusion Probabilistic Models (DDPMs) — in simulating a von Kármán vortex street around a fixed cylinder projected into 2D, as well as a real-world experimental dataset of the wake flow of a cylinder array. Training data was obtained by means of LES in the simulated case and Particle Image Velocimetry (PIV) in the experimental case. We evaluate each model’s ability to capture the statistical properties and spatial structures of the turbulent flow. Our results demonstrate that DDPMs and DCGANs effectively replicate all flow distributions, highlighting their potential as efficient and accurate tools for turbulence surrogacy. We find a strong argument for DCGANs, as although they are more difficult to train (due to problems such as mode collapse), they show the fastest inference and training time, require less data to train compared to VAEs and DDPMs, and provide results most closely aligned with the input stream. In contrast, VAEs train quickly (and can generate samples quickly) but do not produce adequate results, and DDPMs, whilst effective, are significantly slower in both inference and training.