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 (VAE), Deep Convolutional Generative Adversarial Networks (DCGAN), and Denoising Diffusion Probabilistic Models (DDPM) - 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 DDPM and DCGAN effectively replicate all flow distributions, highlighting their potential as efficient and accurate tools for turbulence surrogacy. We find a strong argument for DCGAN, 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 VAE and DDPM, and provide the results most closely aligned with the input stream. In contrast, VAE train quickly (and can generate samples quickly) but do not produce adequate results, and DDPM, whilst effective, are significantly slower at both, inference and training time.

翻译：湍流数值模拟因其复杂性和高昂的计算成本，在流体动力学领域面临重大挑战。高分辨率技术如直接数值模拟（DNS）和大涡模拟（LES）通常计算代价过高，尤其对于技术相关的问题而言。机器学习，特别是生成式概率模型的最新进展，为湍流替代提供了有前景的替代方案。本文研究了三种生成模型——变分自编码器（VAE）、深度卷积生成对抗网络（DCGAN）和去噪扩散概率模型（DDPM）——在模拟投射到二维平面的固定圆柱体周围冯·卡门涡街，以及一个圆柱阵列尾流的真实世界实验数据集中的应用。训练数据在模拟案例中通过LES获得，在实验案例中通过粒子图像测速（PIV）获得。我们评估了每种模型捕捉湍流统计特性和空间结构的能力。我们的结果表明，DDPM和DCGAN能有效复现所有流动分布，凸显了它们作为高效、准确的湍流替代工具的潜力。我们发现DCGAN具有强有力的优势：尽管其训练更为困难（由于模式崩溃等问题），但其推理和训练时间最快，与VAE和DDPM相比需要更少的训练数据，并且提供的结果与输入流场最为吻合。相比之下，VAE训练快速（且能快速生成样本），但无法产生足够好的结果；而DDPM虽然有效，但其推理和训练时间均显著更长。