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

FREESIA proposes a covariance-aware posterior transport method for data assimilation in complex dynamical systems. The approach tackles the challenge of accurate multimodal posterior inference under high-dimensional and sparse observation conditions, particularly for nonlinear or non-injective observation operators. By combining ensemble filtering scalability with expressive generative modeling, FREESIA provides a principled framework for state estimation in geophysical applications such as weather prediction and ocean state estimation.