发表机构
University of Stuttgart; Stuttgart Center for Simulation Science; Institute of Aerospace Thermodynamics（斯图加特大学; 斯图加特模拟科学中心; 航空热力学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对湍流数据同化，提出一种原则性生成式框架，在干净状态空间同化观测并显式引入观测误差协方差，在Lorenz-63和二维瑞利-贝纳德对流中验证了其有效性与物理合理性。
AI 中文摘要
湍流具有高度混沌性，这使得其瞬时状态难以预测。数据同化旨在通过将物理求解器的预测与系统的部分观测相结合来减少这种预测不确定性。传统的数据同化方法，如集合方法和变分方法，可能因高保真求解器的评估以及变分方法中的伴随计算而产生高昂的计算成本。近年来，生成式扩散模型已被探索用于解决流体力学中的逆问题，展示了其在数据同化方面的潜力。然而，现有的基于扩散的方法通常使用自由参数而非规定的观测误差协方差来控制先验与似然之间的平衡，偏离了数据同化的贝叶斯公式。我们提出了一个原则性生成式数据同化框架，其中观测在干净状态空间中被同化，并且规定的观测误差协方差通过集合卡尔曼更新显式地进入。在Lorenz-63系统中，所提出的方法相比其他考虑的基于扩散的后验采样方法，产生了更低的轨迹误差和方程残差，尽管其集合低估了后验不确定性。在二维瑞利-贝纳德对流中，生成的场在大尺度上恢复了直接数值模拟参考的统计特性，偏差仅限于较小尺度。这些结果表明，该框架能够产生物理上合理的湍流场，表明其在更具挑战性的湍流应用中的潜力。
英文摘要
Turbulent flows are highly chaotic, which makes their instantaneous states difficult to predict. Data assimilation aims to reduce this predictive uncertainty by synthesizing the predictions of a physical solver with partial observations of the system. Traditional data assimilation methods such as ensemble and variational approaches can incur substantial computational cost through evaluations of high-fidelity solvers and, for variational methods, adjoint calculations. Recently, generative diffusion models have been explored in the solution of inverse problems in fluid mechanics, demonstrating their potential for data assimilation. However, existing diffusion-based methods often use free parameters instead of the prescribed observation-error covariance to control the balance between the prior and likelihood, departing from the Bayesian formulation of data assimilation. We propose a framework for principled generative data assimilation in which observations are assimilated in the clean-state space and the prescribed observation-error covariance enters explicitly through an ensemble Kalman update. In the Lorenz-63 system, the proposed method yields a lower trajectory error and equation residual than the other diffusion-based posterior sampling methods considered, although its ensemble underestimates the posterior uncertainty. In two-dimensional Rayleigh-Bénard convection, the generated fields recover the statistics of the direct numerical simulation reference at large scales, with deviations confined to the smaller scales. These results suggest that the framework can produce physically plausible turbulent flow fields, indicating its potential for more challenging turbulent flow applications.
