AI Speed Test Finds GANs Beat Diffusion Models as Turbulence Surrogates

Turbulence is one of the hardest problems in fluid dynamics, and the simulations needed to capture it are among the most expensive in computational science. A new open-access study published in Computational Science and Engineering on 15 September 2026 puts three leading generative artificial intelligence models head to head to find out which one can stand in for those costly simulations — and the answer, somewhat against the current tide of the machine learning field, is the generative adversarial network.

Their benchmark cases were a von Kármán vortex street behind a fixed cylinder, computed with Large Eddy Simulation (LES), and a real experimental dataset of the wake behind an array of seven cylinders measured with particle image velocimetry (PIV).

The stakes are high because scale-resolving techniques such as Direct Numerical Simulation and LES are generally not computationally affordable for technologically relevant problems. The LES dataset used in this study alone was produced on a high-performance computing cluster with 20 nodes of 28 cores each, taking roughly 20 days of computation — about 1440 core weeks — on a grid of approximately 15 million cells. Once a generative model is trained, however, producing a new sample of the flow field takes milliseconds to seconds, opening the possibility of generating vast statistical ensembles of turbulent states that would be impractical to obtain with traditional simulation.

The numerical test case was the flow around a circular cylinder at a Reynolds number of 3900, a classical benchmark exhibiting vortex shedding and a Kármán vortex street in the wake. The team simulated 25,000 time steps after initial transients, corresponding to roughly 1.45 seconds of physical time, and sampled snapshots at 68.9 Hz. The velocity fields were converted into two-dimensional grayscale images of the fluctuating velocity magnitude, yielding 100,000 images at 1000 by 600 pixel resolution. The experimental case came from a water channel with cylinders of 1 millimetre diameter, a flow velocity of 133 millimetres per second and a Reynolds number of about 100 based on a single cylinder, recorded at 200 frames per second over 15 seconds, producing 3000 images at 138 by 231 resolution.

To judge quality, the researchers used physics-based metrics rather than image-similarity scores alone: the mean local velocity fluctuation magnitude and its variance, evaluated across progressively larger portions of the downstream wake, from a small near-wake region directly behind the cylinder out to the full wake. The evaluation used 5000 LES snapshots and 5000 images generated by each model for the single-cylinder case, and 3000 PIV snapshots and 3000 synthesized images for each cylinder-array configuration. The authors are careful to note that no method can reproduce the exact turbulent flow for a given set of initial conditions; the models approximate the statistics of the LES and PIV data, not the flow itself.

The results were clear on the weakest performer. The VAE, a lighter model with about 4 million parameters, reproduced the large-scale wake location but underestimated the amplitude of local velocity fluctuations and underrepresented small-scale vortical structures. In the metric comparisons it systematically overestimated the mean local fluctuation magnitude while underpredicting the variance, failing to capture both the average turbulent intensity and the statistical fluctuations associated with coherent and small-scale turbulence. The VAE is fast — it can generate one sample in 0.0003 seconds — but the authors conclude that its output quality simply does not reach the level of the LES data.

The contest between the DCGAN and the DDPM was far closer. Both synthesized turbulent flow that the authors describe as agreeing excellently with the LES flow at the visual level and by the physics-based metrics. In the near-wake region the DCGAN slightly outperformed the DDPM in reproducing areas of high-intensity velocity fluctuations, capturing peaks and inflection points in the variance distributions. In the far wake, however, the picture reversed: the DCGAN better reproduced the overall shape of the variance curve but underestimated high-intensity turbulence more than the DDPM, which retained somewhat higher fidelity for intense fluctuations further downstream. Both models tended to underestimate the highest-intensity fluctuations in the final 25% of the far wake, and both introduced small artificial fluctuations in regions that should remain laminar, an effect that was smaller for the DDPM.

The experimental PIV data added a further twist. For the two cylinder-array configurations tested, both the DCGAN and the DDPM closely matched the statistical properties of the measured flow, and the DCGAN captured the characteristic small-scale fluctuations of the PIV data — including, notably, the inherent measurement noise, which the model apparently learned to reproduce as a feature of realistic samples. The authors see this as evidence that these approaches can robustly handle experimental noise and variability, broadening their potential impact beyond purely numerical datasets.

Where the DCGAN decisively pulled ahead was computational cost. Although it was trained for more than ten times as many epochs as the VAE and DDPM, it trained fastest, on a single GPU, and needed only 0.05% of the full dataset — the first 5000 images of the cylinder dataset — without losing generalizability, while the VAE and DDPM required all 100,000 images. The DDPM, built with attention and an exponential moving average shadow model, has over 135 million parameters. At inference time the DCGAN generated one snapshot in 0.001 seconds, while the DDPM required 36.3 seconds per snapshot — a speed difference of more than a factor of 1000. The VAE was faster still at 0.0003 seconds per sample, but its inadequate output quality rules it out. The authors stress that these figures are wall-clock inference times and are not related to physical time scales of the flow.

The broader message is a challenge to prevailing fashion. While much of the machine learning community is moving towards diffusion and flow-matching models, buoyed by successes such as Stable Diffusion in other domains, this study finds in favour of GANs for turbulence. The authors argue that their work places at least one hyperparameter of machine learning for turbulence — the model architecture — on scientific footing, and note they are among the first to train generative models on a high-fidelity experimental dataset. They caution that their models capture no temporal dependencies, since training was performed without a temporal component, producing temporally independent state snapshots. Still, they conclude that DCGANs and their extended variations remain highly promising for turbulence modeling, while DDPMs, though far less efficient, are still significantly faster than LES and should not be completely discarded. Both the LES and PIV datasets, along with the training and evaluation code, have been made publicly available on Zenodo and GitHub.

Subject of Research: Comparing generative AI models as fast surrogates for turbulent flow simulation and experimental measurement

Article Title: Comparison of generative learning methods as turbulence surrogates

Article References: Drygala, C., Ross, E., Sharifi Ghazijahani, M., Cierpka, C., di Mare, F., & Gottschalk, H. (2026). Comparison of generative learning methods as turbulence surrogates. Computational Science and Engineering, 3(1), Article 8. https://doi.org/10.1007/s44207-026-00017-8

Image Credits: AI Generated

DOI: 10.1007/s44207-026-00017-8

Keywords: turbulence, generative adversarial networks, diffusion models, variational autoencoders, machine learning, fluid dynamics, Large Eddy Simulation, particle image velocimetry, cylinder wake flow, computational cost, surrogate modeling, Comparison