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math.NA2026
Covariance-Informed Ensemble Score Filtering: Embedding Localized Covariance Geometry into Score-Based Transport
Siming Liang, Peter Jan van Leeuwen, Hristo G. Chipilski +3
Background-error covariance models are central to atmospheric data assimilation because they spread partial observational information across space, variables, and dynamically coupl…
math.NA2026
From Variational Optimization to Flow-Based Transport: Posterior-Geometry Regularization for Ill-Conditioned Data Assimilation
Siming Liang, Feng Bao, Hristo G. Chipilski +2
Variational data assimilation computes a Bayesian update through optimization on a fixed posterior geometry, whose conditioning is determined by the prior covariance and the observ…