State-observation augmented diffusion model for nonlinear assimilation

2024-07-31

arXiv.org

AI Summary

Classical data assimilation methods struggle to accurately approximate the true posterior in highly nonlinear systems. To address this, we propose the State-Observation Augmented Diffusion (SOAD) model, which jointly models the generative process of states and observations. Crucially, we provide the first rigorous proof that SOAD’s marginal posterior exactly equals the true posterior—overcoming a fundamental theoretical limitation of conventional score-matching approaches in nonlinear settings. SOAD unifies physical state-space modeling and observation operator embedding within a diffusion probabilistic framework, enabling deep integration of physics-based constraints and data-driven learning via joint training of denoising score estimation and variational inference. Evaluated on multiple strongly nonlinear assimilation benchmarks, SOAD consistently outperforms existing data-driven methods, achieving superior posterior estimation accuracy and robustness.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Addresses high nonlinearity in data assimilation models
• Proposes SOAD for improved state variable estimation
• Ensures SOAD matches true posterior distribution theoretically

Innovation

• State-Observation Augmented Diffusion model
• Data-driven assimilation technique
• Marginal posterior matches true distribution