Bayesian data assimilation framework combines models and noisy observations
A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants
Machine LearningComputational Engineering, Finance, and Science
Summary
Combining mathematical models with noisy sensor data to make better predictions is important but often hard, especially when dealing with complex systems. The authors present a new method that uses pretrained machine learning models to efficiently sample from the updated predictions without needing additional training. This approach unifies different techniques for refining predictions and offers practical ways to handle high-dimensional data. They tested their method on examples including fluid dynamics and air flow in cities, showing it works well even with thousands of variables.
What this means in practice
- •For weather forecast teams: Improve forecasting accuracy by integrating complex physical models and noisy sensor measurements without retraining existing machine learning components.
- •For urban airflow engineers: Simulate and update predictions of city airflow conditions using high-dimensional data assimilated efficiently from sensors and models.
Authors
Nikolaj T. Mücke, Benjamin Sanderse
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.