← Back to all news
arXiv Machine Learning By Nikolaj T. M\"ucke, Benjamin Sanderse

A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants

Read the original on arXiv Machine Learning →

A new framework for Bayesian data assimilation is presented that leverages pretrained stochastic interpolants, flow matching, and diffusion models as posterior samplers without retraining. By conditioning the interpolant path on observations, a shared likelihood‑score correction is applied to the drift or velocity, unifying stochastic and deterministic sampling methods. The approach yields exact posterior samples when the intermediate likelihood score is known, and practical approximations use a Gaussian surrogate with bias‑corrected mean and inflated covariance, enabling tractable high‑dimensional applications such as linear‑Gaussian dynamics, stochastic Navier‑Stokes, and urban airflow simulations with up to $O(10^4)$ degrees of freedom.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Sep 23

FREESIA: Covariance-Aware Posterior Transport for Expressive and Scalable Data Assimilation

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
multimodal
More like this →
arXiv Machine Learning
Sep 24

PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation

PR‑Smoother is an amortized smoothing method that preserves the explicit use of a prescribed simulator in both the evidence lower bound and the variational family. It learns only future‑conditioned corrections to the simulator’s rollout, yielding a non‑Gaussian smoothing distribution that can jointly infer state, parameters, and sensor bias from observations alone. The approach recovers the exact smoother in deterministic and linear‑Gaussian limits and has been shown to capture multimodal posteriors in Lorenz‑96 and scale to 16,384‑dimensional Kolmogorov flow.

By Yuta Tarumi
multimodalsafety
More like this →
arXiv Machine Learning
Aug 31

Prequential posteriors

The paper introduces prequential posteriors, a Bayesian approach that uses a predictive‑sequential loss function to update deep generative forecasting models (DGFMs) when new data arrive. By adopting a consistency notion suitable for model misspecification, the authors prove that both the loss minimizer and the posterior concentrate on parameters with optimal predictive performance. Scalable inference is achieved with parallelisable waste‑free sequential Monte Carlo samplers that employ preconditioned gradient kernels, and the method is validated on synthetic and real meteorological time‑series data.

By Shreya Sinha-Roy, Richard G. Everitt, Christian P. Robert, Ritabrata Dutta
reinforcement-learning
More like this →