GenAI meets Turbulence: From Super-resolution to Forecasting and Full Field Reconstruction from Sparse Observations

Neural operators (NOs) are powerful PDE surrogates, but their standard L2/MSE training smooths out the high‑frequency, low‑energy structures that matter in turbulence. We tackle three practical problems where a vanilla NO breaks down: (1) super‑resolving low‑resolution Schlieren images of an impinging jet, (2) forecasting 3D homogeneous isotropic turbulence for five eddy‑turnover times from only 160 training snapshots, and (3) reconstructing the turbulent wake of a cylinder from sparse, PIV‑like observations from 150 training samples. For (1) and (2), adversarially training a NO with a GAN‑style discriminator (adv-NO) recovers the missing high‑wavenumber content without the iterative cost of diffusion models, and outperforms VAE, and physics‑informed NO baselines. For (3), both NO and adv-NO fail to reconstruct unseen regions, whereas a conditional diffusion model zero‑shot reconstructs full 3D fields from random points, masked patches, or limited observation subdomains. Our systematic study offers a practical roadmap for selecting appropriate GenAI surrogates for turbulence tasks.