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:2609.39626v1 Announce Type: cross
Abstract: Ensemble smoothers are the most successful and efficient techniques currently available for history matching. However, because these methods rely on...
By Marcio A. Sampaio, Paulo H. Ranazzi, Martin J. Blunt
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
By Yuanzhe Wang, Alexandre M. Tartakovsky
arXiv:2508. 13313v4 Announce Type: replace-cross Abstract: Data assimilation (DA) estimates a dynamical system's state from noisy observations.
By Taos Transue, Bohan Chen, So Takao, Bao Wang
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
arXiv:2602.02832v4 Announce Type: replace
Abstract: Forward forecasting and data assimilation are the two important aspects in physical simulation: one propagates the state forward, the other recover...
By Rares Grozavescu, Etienne Meunier, Pengyu Zhang, Mark Girolami