Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving stability when generalizing to longer rollout horizons remains a persistent challenge for learned PDE solvers. We address this challenge by introducing a fully data-driven fluid solver that utilizes an autoregressive rollout based on conditional diffusion models. We show that this approach offers clear advantages in terms of rollout stability compared to other learned baselines. Remarkably, these improvements in stability are achieved without compromising the quality of generated samples, and our model successfully generalizes to flow parameters beyond the training regime. Additionally, the probabilistic nature of the diffusion approach allows for inferring predictions that align with the statistics of the underlying physics. We quantitatively and qualitatively evaluate the performance of our method on a range of challenging scenarios, including incompressible and transonic flows, as well as isotropic turbulence.

基于条件扩散模型的全数据驱动流体求解器通过自回归预测实现了稳定的长期复现性，同时能够推广到训练范围之外的流动参数。

利用自回归条件扩散模型进行湍流流动模拟