Generative AI for efficient statistical computation of fluids

We present GenCFD, a generative modeling approach for fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. While motivated from conditional score-based diffusion models, GenCFD is both empirically and theoretically validated on generating turbulent flows. Extensive numerical experimentation of challenging three-dimensional fluids demonstrates that GenCFD provides an accurate approximation of relevant statistical quantities of interest while also efficiently generating high-quality realistic samples of such flows. Moreover, we present rigorous theoretical results on analytically tractable models with mathematically relevant features of turbulent fluid flows. The analysis uncovers the mechanism underlying the success of the diffusion modeling approach. In particular, we highlight the importance of modeling distributions by GenCFD, while the mean-square-loss used by the deterministic machine learning approaches fails to accurately characterize statistical features of chaotic dynamics.