AECSF: Adaptive Ensemble Conditional Score Filtering for High‑Dimensional Nonlinear Data Assimilation proposes a training‑free adaptive ensemble conditional score filter that constructs an analytically tractable score estimator using the conditional Tweedie identity. The method employs a shared adaptive weighted proposal ensemble to efficiently estimate conditional means for each noisy reverse particle, updating the proposal within the same reverse‑diffusion run. Theoretical analysis characterizes when a fixed weighted proposal yields the exact noisy posterior score and bounds the error between conditional‑mean estimation and reverse‑sampling endpoint error, while numerical experiments show improved posterior sampling and nonlinear filtering accuracy in high‑dimensional problems with limited forecast ensembles.
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: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...
arXiv:2607. 01012v1 Announce Type: new Abstract: Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications.
arXiv:2508. 13313v4 Announce Type: replace-cross Abstract: Data assimilation (DA) estimates a dynamical system's state from noisy observations.
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...
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...
The paper introduces the Belief Flow Filter (BFF), a generative filtering framework that encodes the evolving posterior distribution directly into flow matching model weights and updates them via test‑time gradient descent. By avoiding particle representations and Gaussian assumptions, BFF aligns structurally with Bayesian filtering and targets the recursive filtering operator. Empirical results on five physical systems—including chaotic dynamics, sparse observations, and a tokamak plasma estimation task—show that BFF outperforms existing methods in most benchmark metrics.
arXiv:2609.35944v1 Announce Type: new Abstract: Data Assimilation (DA) aims to recover the full state of a dynamical system that is only partially observed. A solution is to use Score-based models to...
arXiv:2607. 12975v1 Announce Type: cross Abstract: Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations.
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.
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:2605. 29072v2 Announce Type: replace Abstract: Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management.