State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics

TL;DR

This paper introduces the SOAD model, a generative approach that enhances nonlinear data assimilation by integrating state and observation information, with proven theoretical advantages and improved empirical performance.

Contribution

The paper proposes the SOAD model, a novel generative framework that effectively handles nonlinear data assimilation with unknown dynamics, backed by theoretical proof and empirical validation.

Findings

SOAD's marginal posterior matches the true posterior under mild assumptions.

The model demonstrates improved performance over existing data-driven methods.

Theoretical analysis confirms SOAD's advantages in nonlinear assimilation.

Abstract

Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical and observational models. To address this challenge, a novel generative model, termed the State-Observation Augmented Diffusion (SOAD) model is proposed for data-driven assimilation. The marginal posterior associated with SOAD has been derived and then proved to match the true posterior distribution under mild assumptions, suggesting its theoretical advantages over previous score-based approaches. Experimental results also indicate that SOAD may offer improved performance compared to existing data-driven methods.