Bayesian inference for geophysical fluid dynamics using generative models

TL;DR

This paper introduces a novel data assimilation method using diffusion generative models to improve model calibration and predictive accuracy in high-dimensional geophysical fluid dynamics, significantly reducing computational costs.

Contribution

It develops a new calibration approach with diffusion generative models that enables efficient data assimilation and model reduction in complex, nonlinear geophysical systems.

Findings

Enhanced predictive accuracy with generative model-based data assimilation

Reduced computational complexity in high-dimensional systems

Effective handling of multimodal distributions in state estimation

Abstract

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied in fields such as meteorology, oceanography, and environmental science, where the dynamic nature of systems demands continuous updates to model states. However, the calibration of models in these high-dimensional, nonlinear systems poses significant challenges. In this paper, we explore a novel calibration methodology using diffusion generative models. We generate synthetic data that statistically aligns with a given set of observations (in this case the increments of the numerical approximation of a solution of a partial differential equation). This allows us to efficiently implement a model reduction and assimilate data from a reference system state modeled by a highly resolved numerical solution of the rotating shallow water equation of order 104 degrees of freedom into a stochastic system having two orders of magnitude less degrees of freedom. To do so, the new samples are incorporated into a particle filtering methodology augmented with tempering and jittering for dynamic state estimation, a method particularly suited for handling complex and multimodal distributions. This work demonstrates how generative models can be used to improve the predictive accuracy for particle filters, providing a more computationally efficient solution for data assimilation and model calibration.