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: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.
arXiv:2607. 12975v1 Announce Type: cross Abstract: Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations.
Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations. Many observation mechanisms, however, are many-to-one, implicit, non-smooth, or accessible only through simulation, and need not provide the residual structures or likelihood guidance required by existing ensemble filters.
arXiv:2610.32148v1 Announce Type: cross Abstract: Background-error covariance models are central to atmospheric data assimilation because they spread partial observational information across space, v...
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.
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: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...
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 presents a lightweight retraining strategy for a parameterized Reduced Order Model (ROM) that achieves full‑model accuracy using only a fraction of the computational effort and sparse observations. The ROM architecture combines a Variational Autoencoder for dimensionality reduction with a transformer network that evolves latent states while accounting for the Reynolds number as an external control variable. By leveraging the probabilistic VAE, the method generates trajectory ensembles and uncertainty estimates, and adapts to out‑of‑sample parameters through sparse data assimilation with an ensemble Kalman filter, focusing retraining on the autoencoder to correct latent manifold distortions.
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.
arXiv:2606. 26497v1 Announce Type: new Abstract: Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system, given observations, in an online fashion.
arXiv:2610.03314v1 Announce Type: cross Abstract: Flow- and diffusion-based generative models have recently emerged as flexible and highly efficient forecasting models for dynamical systems. When com...