Learning local-to-global flow super-resolution with generative AI

High-resolution flow measurements, such as those obtained from experimental particle image velocimetry (PIV), are often constrained to a small field of view due to optical limitations. This presents a challenge for reconstructing fine-scale flow structures over large domains. We present a generative learning framework for reconstructing high-resolution fluid flow fields from low-resolution measurements, leveraging only localized high-fidelity data during training. Given access to high-resolution flow data confined to a small subregion, obtained from either direct numerical simulation (DNS) or high-resolution experimental PIV, we train a conditional generative model to learn a mapping from coarse to fine-scale flow features. Once trained, the model is applied globally to reconstruct the high-resolution flow field at the entire domain using only the low-resolution counterpart. We explore and compare both generative adversarial networks (GANs) and diffusion models conditioned on low-resolution measurements to learn the underlying statistics of turbulence and enforce physical consistency at the entire domain. We demonstrate the application of our framework for flow past cylinder problem at multiple Reynolds numbers.