发表机构
Tongji University; University of South Carolina（同济大学; 南卡罗来纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维稀疏观测下非线性数据同化的多峰后验推断难题，提出免训练、渐近精确的协方差感知后验传输方法，嵌入交叉协方差并校正后验，在多个基准上显著提升精度。
AI 中文摘要
数据同化旨在基于观测数据推断复杂动力系统的状态。然而，在非线性或非注入式观测算子所引发的多峰后验分布下，进行准确推断在高维和稀疏观测条件下仍是一个关键挑战。集成滤波器可扩展到高维，但受限于严格的分布假设，而免训练生成滤波器（如EnSF、EnFF）缓解了这一限制，但可能引入结构误差并在稀疏观测下阻碍信息传播。为解决这些问题，我们提出了一种免训练、渐近精确的后验传输方法。首先，设计了一种协方差感知的后验传输方案，将预报交叉协方差嵌入基于流的传输中，在保留非高斯后验结构的同时准确恢复未观测状态。此外，该方法将可处理的观测自适应提议与后验校正相结合，确保对非线性后验分布的准确近似。最后，我们建立了相应的后验流理论，由此推导出所提方法相对于有限集成代理的渐近精确性以及Wasserstein误差界。在Double-Well、Lorenz-96和Kolmogorov流上的实验表明，所提方法能够捕捉复杂的后验结构，并在稀疏、非线性和非注入式观测下保持准确性。在稀疏非注入式设置中，相对于最佳基线，其RMSE降低了56%。
英文摘要
Data assimilation aims to infer the state of complex dynamical systems based on observational data. However, accurate inference of the multimodal posteriors induced by nonlinear or non-injective observation operators remains a key challenge under high-dimensional and sparse observation conditions. Ensemble filters scale to high dimensions but are confined by restrictive distributional assumptions, while training-free generative filters (e.g., EnSF, EnFF) alleviate this limitation but may introduce structural errors and hinder information propagation under sparse observations. To address these issues, we propose a training-free, asymptotically exact posterior transport method. Firstly, a covariance-aware posterior transport scheme is designed, which embeds the forecast cross-covariance into flow-based transport and accurately recovers unobserved states while preserving the non-Gaussian posterior structure. Furthermore, the method combines a tractable observation-adaptive proposal with posterior correction, ensuring accurate approximation of the nonlinear posterior distribution. Finally, we establish the corresponding posterior flow theory, from which the asymptotic exactness of the proposed method relative to finite-ensemble surrogates and the Wasserstein error bound are derived. Experiments on Double-Well, Lorenz-96, and Kolmogorov flow show that the proposed method captures complex posterior structure and remains accurate under sparse, nonlinear, and non-injective observations. In the sparse non-injective setting, it reduces RMSE by 56% relative to the best baseline.
