Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving temporal stability when generalizing to longer rollout horizons remains a persistent challenge for learned PDE solvers. In this work, we analyze if fully data-driven fluid solvers that utilize an autoregressive rollout based on conditional diffusion models are a viable option to address this challenge. We investigate accuracy, posterior sampling, spectral behavior, and temporal stability, while requiring that methods generalize to flow parameters beyond the training regime. To quantitatively and qualitatively benchmark the performance of various flow prediction approaches, three challenging 2D scenarios including incompressible and transonic flows, as well as isotropic turbulence are employed. We find that even simple diffusion-based approaches can outperform multiple established flow prediction methods in terms of accuracy and temporal stability, while being on par with state-of-the-art stabilization techniques like unrolling at training time. Such traditional architectures are superior in terms of inference speed, however, the probabilistic nature of diffusion approaches allows for inferring multiple predictions that align with the statistics of the underlying physics. Overall, our benchmark contains three carefully chosen data sets that are suitable for probabilistic evaluation alongside various established flow prediction architectures.

翻译：湍流模拟在众多应用领域中至关重要，基于机器学习的求解器正日益凸显其重要性。然而，对于学习型偏微分方程求解器而言，在推广至更长推演时间范围时保持时间稳定性仍是一个持续存在的挑战。本研究旨在分析基于条件扩散模型的自回归推演框架构建的完全数据驱动流体求解器是否为应对这一挑战的可行方案。我们在要求方法泛化至超出训练范围的流动参数的同时，系统评估了其精度、后验采样特性、谱行为及时间稳定性。为定量与定性评估各类流动预测方法的性能，我们采用了三种具有挑战性的二维场景，包括不可压缩流、跨音速流以及各向同性湍流。研究发现，即使基于简单的扩散方法也能在精度与时间稳定性方面超越多种现有流动预测方法，其表现与训练时展开等先进稳定化技术相当。传统架构在推理速度方面具有优势，但扩散方法的概率特性允许推断出多个符合底层物理统计规律的预测结果。总体而言，本基准测试包含三个精心设计的数据集，适用于结合多种成熟流动预测架构进行概率性评估。