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This paper introduces LD-EnFF, a novel Bayesian filtering framework that leverages latent dynamics and variational autoencoders to solve data assimilation problems in high-dimensional nonlinear systems. By performing forecasting and likelihood evaluation in a compact latent space, the method significantly reduces computational costs while improving accuracy on benchmarks like atmospheric modeling and tsunami propagation. It represents a meaningful advancement in applying machine learning techniques to handle sparse observations within complex dynamical systems.
LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations
arXiv:2610.04034v1 Announce Type: new 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.
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.
Machine Learning (cs.LG)
arXiv:2610.04034 [cs.LG]
(or arXiv:2610.04034v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.04034 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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