Turbulent flows are well known to be chaotic and hard to predict; however,
their dynamics differ between two and three dimensions. While 2D turbulence
tends to form large, coherent structures, in three dimensions vortices cascade
to smaller and smaller scales. This cascade creates many fast-changing,
small-scale structures and amplifies the unpredictability, making
regression-based methods infeasible. We propose the first generative model for
forced turbulence in arbitrary 3D geometries and introduce a sample quality
metric for turbulent flows based on the Wasserstein distance of the generated
velocity-vorticity distribution. In several experiments, we show that our
generative diffusion model circumvents the unpredictability of turbulent flows
and produces high-quality samples based solely on geometric information.
Furthermore, we demonstrate that our model beats an industrial-grade numerical
solver in the time to generate a turbulent flow field from scratch by an order
of magnitude.

本文提出了一种基于生成扩散模型的新方法，用于固定几何形状中的强制湍流生成，同时引入了一种基于 Wasserstein 距离的湍流样本质量度量方法，实验证明该方法能以高质量样本为代价规避湍流的不可预测性，并且在从头开始生成湍流场的时间方面击败了工业级数值求解器一个数量级。