arXiv Machine Learning

Improving Ensemble Filters with Flow Matching

arXiv Machine Learning
Sep 23

FREESIA: Covariance-Aware Posterior Transport for Expressive and Scalable Data Assimilation

The paper introduces FREESIA, a training‑free, covariance‑aware posterior transport method for data assimilation that embeds forecast cross‑covariance into a flow‑based transport to recover unobserved states while preserving non‑Gaussian posterior structure. It combines an observation‑adaptive proposal with posterior correction, providing an asymptotically exact approximation of nonlinear posteriors and a Wasserstein error bound. Experiments on Double‑Well, Lorenz‑96, and Kolmogorov flow demonstrate that FREESIA captures complex posterior structures and achieves up to a 56% reduction in RMSE compared to the best baseline in sparse, nonlinear, non‑injective observation scenarios.

By Shiwei Ni, Yangwen Zhang, Hang Qi, Xiaofei Guan, Lili Ju
arXiv Machine Learning
Jun 11

Neural ensemble Kalman filter: Data assimilation for compressible flows with shocks

arXiv:2602. 23461v2 Announce Type: replace-cross Abstract: Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks.

By Xu-Hui Zhou, Lorenzo Beronilla, Michael K. Sleeman, Hangchuan Hu, Matthias Morzfeld, Andrew M. Stuart, Tamer A. Zaki