发表机构
School of Computation, Information and Technology, Technical University of Munich（慕尼黑工业大学计算、信息与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建StocBench基准，对比测试多种生成模型与少步方法在随机流体流动概率预测中的性能，明确不同模型在随机与确定性任务、不同推理预算下的表现差异。
AI 中文摘要
我们针对随机流体流动的概率预测，对基于传输的生成模型以及基于蒸馏的少步方法进行了基准测试，特别关注在有限推理预算下的性能。所有方法均在带有随机强迫的二维Kolmogorov流动上进行评估。我们针对大型模拟参考集测量单步分布准确性，并通过涡量谱评估自回归回滚过程中是否保持不变测度。在随机任务中，Flow Matching在高推理预算下实现最准确的单步条件分布，而二阶指数积分器DPM-2在极低的NFE下表现最强。少步蒸馏方法与多步方法具有竞争力，且能特别好地保持涡量谱。确定性控制任务中，预测区间内的强迫是可观测的，该任务将偶然不确定性与认知不确定性区分开。模型性能在两种场景间不具可迁移性：蒸馏模型在随机任务上具有竞争力，但在控制任务上准确性最低。在随机场景中，如DDPM这类随机扩散采样器在回滚过程中能更好地保持涡量谱，而在确定性场景中，如DDIM和DPM-2这类确定性采样器表现出更好的谱保持能力。
英文摘要
We benchmark transport-based generative models as well as distillation-based few-step methods for the probabilistic forecasting of stochastic fluid flows, with a particular focus on performance under limited inference budgets. All methods are evaluated on a two-dimensional Kolmogorov flow with stochastic forcing. We measure one-step distributional accuracy against large simulated reference ensembles and assess whether the invariant measure is preserved during autoregressive rollouts via the enstrophy spectrum. On the stochastic task, flow matching achieves the most accurate one-step conditional distribution at high inference budgets, while the second-order exponential integrator DPM-2 is strongest at very low NFE. Few-step distillation methods are competitive with the multi-step methods and preserve the enstrophy spectrum particularly well. A deterministic control task, in which the forcing over the prediction interval is observed, separates aleatoric from epistemic uncertainty. Model performance does not translate between the two settings: the distilled models are competitive on the stochastic task but least accurate on the control task. While stochastic diffusion samplers such as DDPM better preserve the enstrophy spectrum during rollouts in the stochastic setting, deterministic samplers such as DDIM and DPM-2 show better spectral preservation in the deterministic setting.
CommentsCode available at https://github.com/tum-pbs/stocbench
