Speaker
Description
Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. This difficulty arises from the combination of extreme dimensionality, multiscale fluctuations, strong intermittency, and the need to satisfy exact physical constraints, including incompressibility and prescribed mass and momentum fluxes under given boundary conditions. We propose a physics-constrained diffusion model (PCDM) in which some a priori constraints can be incorporated directly into the generative dynamics. Using rotating turbulence as a paradigmatic open problem, with key applications to geophysical contexts, we show that the proposed framework enables stable and statistically faithful synthesis of inertial-range three-dimensional turbulent velocity fields, accurately reproducing anisotropic energy spectra, intermittent statistics, and physical constraints. By contrast, standard denoising diffusion probabilistic models without such constraints exhibit multiscale statistical deviations, violations of physical consistency, and substantially slower training convergence. These results point to broader implications for generative modeling of high-dimensional, physically constrained complex systems.