对比生成模型在随机流体预测中的表现,尤其关注低推理预算下的效果。
StocBench: A Benchmark for Generative Modeling of Stochastic Dynamics
- 基于传输与蒸馏方法,评估生成模型在随机流体中的预测能力。
- 高预算下流匹配最准,极低预算下二阶指数积分器最优。
- 蒸馏模型在随机任务中表现好,但对确定性控制任务不适用。
我们评估基于传输的生成模型以及基于蒸馏的少步方法,在二维柯尔莫戈洛夫随机强迫流体中的概率预测性能,重点关注有限推理预算下的表现。所有方法均在带随机力的二维柯尔莫戈洛夫流上测试。通过大样本模拟参考集衡量单步分布准确性,并利用涡度谱评估自回归滚动过程中不变测度的保持情况。在随机任务中,流匹配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NFE(每步函数调用次数)下表现最佳。少步蒸馏方法与多步方法相当,且对涡度谱的保持尤为出色。另设一个确定性控制任务(预测期内力已知),用于分离随机不确定性与认知不确定性。模型性能在两任务间不具可迁移性:蒸馏模型在随机任务中表现良好,但在控制任务中最不准确。在随机设置中,如DDPM等随机扩散采样器更优地保持了涡度谱;而在确定性设置中,如DDIM和DPM-2等确定性采样器表现更佳。
原文摘要 · Abstract (English)
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.
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