LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations

2026-10-02

AI Summary

This study addresses the challenges of high computational cost and insufficient sparse observational information in data assimilation for high-dimensional nonlinear dynamical systems by proposing the Latent Dynamic Ensemble Flow Filter. This method pioneers the integration of a variational autoencoder-based latent-space surrogate model with flow matching algorithms, performing the prediction and update steps of Bayesian sequential filtering within a low-dimensional latent space to achieve joint state-parameter estimation while circumventing the prohibitive simulation overhead of the full state space. Evaluated on benchmarks including Kolmogorov flow and tsunami propagation, the proposed framework significantly outperforms existing data assimilation algorithms, providing an efficient and robust solution for high-dimensional complex systems.

Abstract

Data assimilation combines model forecasts with noisy, incomplete observations to estimate the evolving state of a dynamical system. Existing methods face two compounding challenges: high-dimensional nonlinear dynamics make repeated forward simulation computationally expensive, while sparse observations provide limited direct information about the full state. To address these challenges, we propose the Latent-Dynamics Ensemble Flow Filter (LD-EnFF), a sequential Bayesian filtering framework that performs both forecast propagation and filtering updates in a compact latent space. LD-EnFF combines a latent dynamics surrogate for ensemble propagation with a variational autoencoder (VAE)-based observation model that evaluates a state-dependent observation likelihood in latent space. At each assimilation step, an ensemble filtering update based on flow matching uses the forecast ensemble and this likelihood to generate posterior samples, jointly updating latent states and uncertain parameters. This design avoids repeated full-state simulation during forecasting and full-field reconstruction during likelihood evaluation. LD-EnFF substantially outperforms a broad range of data assimilation algorithms on benchmarks spanning Kolmogorov flow, tsunami propagation, and atmospheric modeling, all featuring complex dynamics and sparse, noisy observations.

Problem

• Data Assimilation
• High-dimensional Nonlinear Dynamics
• Sparse Observations
• Computational Cost

Innovation

• Latent-Dynamics Ensemble Flow Filter
• Data Assimilation
• Flow Matching
• Variational Autoencoder
• Sparse Observations