发表机构
Oak Ridge National Laboratory; Florida State University; Colorado State University（橡树岭国家实验室; 佛罗里达州立大学; 科罗拉多州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于流的输运方法替代变分优化进行数据同化，通过逐步正则化中间分布的协方差和曲率缓解病态后验几何，数值测试显示其在高维病态问题上更鲁棒且计算成本更低。
AI 中文摘要
变分数据同化通过在固定的后验几何上进行优化来计算贝叶斯更新，该几何的条件数由先验协方差和观测算子决定。在强各向异性、弱观测或高信息量情况下，这种几何可能变得严重病态，导致对求解器设计和预条件处理高度敏感。本研究探索了一种基于流输运的替代计算途径，使用集成分数滤波器作为无需训练的实现。与在整个后验几何上反复优化不同，基于流的更新通过一系列中间分布输运预测分布，这些中间分布的协方差和曲率在到达目标后验之前逐步被正则化。在线性高斯设定中，我们通过扩散后验协方差和相关的时间相关曲率的演化来刻画这一机制，揭示了一条从近似各向同性的参考几何到变分同化所针对的病态后验几何的连续路径。数值压力测试表明，这种几何正则化使基于流的方法对严重病态的敏感性远低于变分方法，而一个异构的10^4维Lorenz-96基准测试则展示了改进的鲁棒性和更低的计算成本。这些结果将后验几何正则化确定为区分基于输运与基于优化的数据同化的关键机制。
英文摘要
Variational data assimilation computes a Bayesian update through optimization on a fixed posterior geometry, whose conditioning is determined by the prior covariance and the observation operator. In strongly anisotropic, weakly observed, or highly informative regimes, this geometry can become severely ill conditioned, leading to substantial sensitivity to solver design and preconditioning. This work investigates an alternative computational route based on flow-based transport, using the ensemble score filter as a training-free realization. Rather than repeatedly optimizing over the full posterior geometry, the flow-based update transports the predictive distribution through a sequence of intermediate distributions whose covariance and curvature are progressively regularized before reaching the target posterior. In the linear-Gaussian setting, we characterize this mechanism through the evolution of the diffused posterior covariance and the associated time-dependent curvature, revealing a continuation from a near-isotropic reference geometry to the ill-conditioned posterior geometry targeted by variational assimilation. Numerical stress tests show that this geometric regularization makes the flow-based method substantially less sensitive to severe ill-conditioning than the variational method, while a heterogeneous $10^4$-dimensional Lorenz-96 benchmark demonstrates improved robustness and lower delivered computational cost. These results identify posterior-geometry regularization as a key mechanism distinguishing transport-based from optimization-based data assimilation.
Comments25 pages, 8 figures, 5 tables
