analiza aiqbench
This research presents a novel framework that leverages pretrained generative models, such as diffusion and flow matching, to perform Bayesian data assimilation without requiring retraining. By unifying stochastic and deterministic sampling methods through observation interpolants, the approach effectively handles high-dimensional, non-Gaussian posteriors in complex physical systems like urban airflow. The method's ability to scale to thousands of degrees of freedom while maintaining tractability marks a significant advancement for integrating AI with computational science.
A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants
arXiv:2610.03396v1 Announce Type: new Abstract: Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without retraining. Conditioning the interpolant path on observations yields a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. The resulting SDEs and ODEs sample the exact posterior when the intermediate likelihood score is known. For practical computation, we approximate this score using a closed-form Gaussian surrogate with a bias-corrected mean and covariance inflated by the model's source covariance. Jacobian-free and ensemble-shared approximations make the method tractable in high dimensions. We evaluate the framework on linear-Gaussian dynamics, stochastic two-dimensional Navier-Stokes, and urban airflow with up to $O(10^4)$ degrees of freedom.
Abstract:Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without retraining. Conditioning the interpolant path on observations yields a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. The resulting SDEs and ODEs sample the exact posterior when the intermediate likelihood score is known. For practical computation, we approximate this score using a closed-form Gaussian surrogate with a bias-corrected mean and covariance inflated by the model's source covariance. Jacobian-free and ensemble-shared approximations make the method tractable in high dimensions. We evaluate the framework on linear-Gaussian dynamics, stochastic two-dimensional Navier-Stokes, and urban airflow with up to $O(10^4)$ degrees of freedom.
Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE)
arXiv:2610.03396 [cs.LG]
(or arXiv:2610.03396v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.03396 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 229 cuvinte
Subiecte conexe
Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Flow-matching
arXiv · 6 aug. 2026
Post-Train NVIDIA Cosmos 3 in One Day Using Agent Skills
NVIDIA · 14 iul. 2026
Beyond Point Forecasts: A Survey on Probabilistic Forecasting for Time Series and Spatiotemporal Data
arXiv · 15 sept. 2026
Bayesian Flow Networks for Offline Trajectory Planning
arXiv · 27 aug. 2026