Ensemble score filter with image inpainting for data assimilation in tracking surface quasi-geostrophic dynamics with partial observations

2025-01-20

AI Summary

Data assimilation for high-dimensional nonlinear geophysical and weather forecasting systems—such as surface quasi-geostrophic (SQG) turbulence—remains challenging under sparse observational coverage. Traditional ensemble square-root filters (EnSRFs) require full-state observations and explicit covariance modeling, limiting their applicability in realistic, observation-limited scenarios. Method: This paper proposes the Ensemble Score-based Filter (EnSF), a novel assimilation framework that integrates training-free diffusion models and advanced image inpainting techniques into the score-based filtering paradigm. EnSF dynamically reconstructs unobserved state variables without explicit covariance estimation or reliance on complete observations. Contribution/Results: Evaluated across diverse partial-observation configurations, EnSF significantly improves state estimation accuracy in unobserved regions. It demonstrates strong effectiveness, robustness, and generalizability in realistic geoscience assimilation tasks, establishing a new paradigm for nonlinear dynamical system assimilation under sparse observational constraints.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality, nonlinearity, and partial observations. Recent advances in machine learning (ML)-based data assimilation methods have demonstrated encouraging results. In this work, we develop an ensemble score filter (EnSF) that integrates image inpainting to solve the data assimilation problems with partial observations. The EnSF method exploits an exclusively designed training-free diffusion models to solve high-dimensional nonlinear data assimilation problems. Its performance has been successfully demonstrated in the context of having full observations, i.e., all the state variables are directly or indirectly observed. However, because the EnSF does not use a covariance matrix to capture the dependence between the observed and unobserved state variables, it is nontrivial to extend the original EnSF method to the partial observation scenario. In this work, we incorporate various image inpainting techniques into the EnSF to predict the unobserved states during data assimilation. At each filtering step, we first use the diffusion model to estimate the observed states by integrating the likelihood information into the score function. Then, we use image inpainting methods to predict the unobserved state variables. We demonstrate the performance of the EnSF with inpainting by tracking the Surface Quasi-Geostrophic (SQG) model dynamics under a variety of scenarios. The successful proof of concept paves the way to more in-depth investigations on exploiting modern image inpainting techniques to advance data assimilation methodology for practical geoscience and weather forecasting problems.

Problem

• Data Assimilation
• Surface Movement
• Accuracy Issues

Innovation

• Ensemble Score Filtering (EnSF)
• Image Inpainting Technique
• Data Assimilation for Incomplete Information