Comparison of Generative Learning Methods for Turbulence Modeling
High-fidelity turbulent flow simulations—such as direct numerical simulation (DNS) and large-eddy simulation (LES)—remain computationally prohibitive for routine engineering applications. This work systematically compares three generative probabilistic models—variational autoencoders (VAEs), deep convolutional generative adversarial networks (DCGANs), and denoising diffusion probabilistic models (DDPMs)—for modeling two-dimensional Karman vortex streets, trained exclusively on LES data. Evaluation is conducted across three dimensions: statistical fidelity, spatial structure preservation, and multiscale dynamical consistency. Results demonstrate that DCGAN achieves the best overall performance in generation fidelity, inference speed, and sample efficiency—accurately reconstructing turbulent fields from limited LES data. DDPM attains higher accuracy but suffers from prohibitively slow inference; VAE trains rapidly yet yields significant structural distortions. This study establishes generative modeling as a novel, high-fidelity, low-cost surrogate paradigm for turbulence, providing a scalable, data-driven methodology for turbulent flow simulation.