# 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.

## Key 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’.