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
This study introduces the first controlled benchmark of generative models for weather data assimilation using real station observations from 11,849 NOAA MADIS stations across the U.S. It evaluates key design choices—diffusion vs. flow matching, pixel vs. latent-space formulations, and inference-time conditioning strategies—against a classical 3D-Var baseline. The benchmark finds that learned generative priors and full-gradient guidance improve RMSE over ERA5, while other design variations offer minimal benefit, especially under sparse observation conditions.
By Ruizhe Huang, Qidong Yang, Jonathan Giezendanner, Sherrie Wang
arXiv:2607. 01012v1 Announce Type: new Abstract: Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications.
By Chandni Nagda, Mayank Shrivastavam Gudrun Thorkelsdottir, Gan Zhang, Morteza Mardani, Arindam Banerjee
arXiv:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.
By Caroline Tatsuoka, Minglei Yang, Dongbin Xiu, Guannan Zhang
arXiv:2608. 02629v1 Announce Type: cross Abstract: The use of variable well perforation and injection strategies can improve the efficiency of geological carbon storage operations.
By Yifu Han, Louis J. Durlofsky
arXiv:2602.23188v2 Announce Type: replace
Abstract: We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while...
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
arXiv:2609.13242v1 Announce Type: cross
Abstract: Subgrid parametrizations of vertical mixing in ocean models depend on free coefficients that cannot be measured directly and must be calibrated again...
By Luben M. C. Cabezas, Sacha Wendling, Aur\`ele Gallard, Gabriel Mouttapa, Julien Le Sommer, Pedro L. C. Rodrigues