Bayesian inference for geophysical fluid dynamics using generative models

TL;DR

The paper introduces a new method using generative models to improve data assimilation in complex geophysical simulations.

Contribution

A novel calibration approach using diffusion generative models for efficient data assimilation in high-dimensional systems.

Findings

Generative models produce synthetic data that align with observed numerical solutions.

The method reduces model complexity while maintaining accuracy in data assimilation.

Particle filtering with synthetic data improves computational efficiency and accuracy.

Abstract

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’.

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