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arXiv:2611.07160v1 Announce Type: new Abstract: Many real-world applications, such as numerical weather prediction or wildfire tracking, involve modeling highly nonlinear dynamical systems that are c...
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.
The paper introduces a feature‑preserving latent‑EnKF for data assimilation of flows with shocks, addressing the failure of traditional EnKF when discontinuities are present. By updating ensembles in a low‑dimensional latent space learned via a coordinate‑conditioned auto‑decoder, the method maintains near‑Gaussian statistics and coherent flow features, enabling shock translation through coordinate morphing rather than superposition. Experiments on Sod shock‑tube, Mach 2 shock‑cylinder, and immersed‑body shape‑inference problems show accurate shock recovery without spurious oscillations.
arXiv:2609.28015v1 Announce Type: cross Abstract: Data assimilation estimates a dynamical state from partial and noisy observations. Classical ensemble filters are efficient but restrict analysis upd...
arXiv:2607. 12975v1 Announce Type: cross Abstract: Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations.
The paper presents an ensemble Kalman–Bucy smoother (EnKBS) for continuous‑time data assimilation of nonlinear dynamical systems, reconstructing conditional distributions from ensemble moments without needing tangent‑linear or adjoint models. It demonstrates that EnKBS achieves exact smoothing mean and covariance in the infinite‑ensemble limit for linear‑Gaussian systems and incorporates regularization techniques like covariance localization and inflation for high‑dimensional problems. The method is applied to Bayesian inference of causal relationships in a dyadic trigger‑feedback model and to an iterative learning algorithm that uncovers the structure and hidden parameters of a reduced‑order model of midlatitude atmospheric circulation, all with small ensembles under partial observations.