Generative AI for fast and accurate statistical computation of fluids
This work addresses the pressing need for efficient statistical computation in fluid dynamics, particularly for turbulent flows, offering a novel generative approach that outperforms deterministic ML methods.
The authors tackled the problem of fast and accurate statistical computation of turbulent fluid flows by developing GenCFD, a generative AI algorithm based on a conditional score-based diffusion model, which demonstrated accurate approximation of statistical quantities and efficient generation of high-quality realistic samples with excellent spectral resolution.
We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional score-based diffusion model. Through extensive numerical experimentation with a set of challenging fluid flows, we demonstrate that GenCFD provides an accurate approximation of relevant statistical quantities of interest while also efficiently generating high-quality realistic samples of turbulent fluid flows and ensuring excellent spectral resolution. In contrast, ensembles of deterministic ML algorithms, trained to minimize mean square errors, regress to the mean flow. We present rigorous theoretical results uncovering the surprising mechanisms through which diffusion models accurately generate fluid flows. These mechanisms are illustrated with solvable toy models that exhibit the mathematically relevant features of turbulent fluid flows while being amenable to explicit analytical formulae. Our codes are publicly available at https://github.com/camlab-ethz/GenCFD.