Bayesian inference for geophysical fluid dynamics using generative models.

Data assimilation plays a crucial role in numerical modelling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. However, calibrating high-dimensional, nonlinear systems remains challenging. This article presents a novel calibration approach using diffusion generative models to produce synthetic data that align with observed numerical solutions of a stochastic partial differential equation. These samples enable efficient model reduction, assimilating data from a high-resolution rotating shallow water equation with 10⁴ degrees of freedom into a reduced stochastic system with significantly fewer degrees of freedom. The synthetic samples are integrated into a particle filtering method, enhanced with tempering and jittering, to handle complex, multi-modal distributions. Our results demonstrate that generative models improve particle filter accuracy, offering a more computationally efficient solution for data assimilation and model calibration.This article is part of the theme issue 'Generative modelling meets Bayesian inference: a new paradigm for inverse problems'.