Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilation

TL;DR

This paper introduces a latent autoencoder ensemble Kalman filter (LAE-EnKF) that improves data assimilation in nonlinear systems by learning a stable linear latent space, enhancing accuracy and stability over traditional methods.

Contribution

The paper proposes a novel LAE-EnKF that reformulates data assimilation in a learned latent space with linear dynamics, ensuring structural consistency and improved performance.

Findings

LAE-EnKF outperforms standard EnKF in nonlinear and chaotic systems.

The method maintains computational efficiency comparable to existing approaches.

Theoretical analysis provides error bounds for learning linear dynamics on manifolds.

Abstract

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the underlying system behavior. In this work, we propose a latent autoencoder ensemble Kalman filter (LAE-EnKF) that addresses this limitation by reformulating the assimilation problem in a learned latent space with linear and stable dynamics. The proposed method learns a nonlinear encoder--decoder together with a stable linear latent evolution operator and a consistent latent observation mapping, yielding a closed linear state-space model in the latent coordinates. This construction restores compatibility with the Kalman filtering framework and allows both forecast and analysis steps to be carried out entirely in the latent space. Compared with existing autoencoder-based and latent assimilation approaches that rely on unconstrained nonlinear latent dynamics, the proposed formulation emphasizes structural consistency, stability, and interpretability. We provide a theoretical analysis of learning linear dynamics on low-dimensional manifolds and establish generalization error bounds for the proposed latent model. Numerical experiments on representative nonlinear and chaotic systems demonstrate that the LAE-EnKF yields more accurate and stable assimilation than the standard EnKF and related latent-space methods, while maintaining comparable computational cost and data-driven.