Dynamical Low-Rank Ensemble Kalman filter for State/Parameter estimation

We propose a Dynamical Low-Rank Ensemble Kalman Filter (DLR-ENKF) for efficient joint state-parameter estimation in high-dimensional dynamical systems. The method extends the DLR-ENKF formulation of arXiv:2509.11210 to the augmented state-parameter framework, tracking the filtering density within a dynamically evolving low-dimensional subspace. Key developments include a time-integration strategy that combines the Basis Update & Galerkin scheme with forecast/analysis discretisation, and a DEIM-based hyper-reduction technique for efficient evaluation of nonlinear terms. We demonstrate the effectiveness, robustness, and computational advantages of the proposed approach on benchmark problems. The results highlight the potential of dynamically evolving reduced bases to achieve accurate filtering and parameter estimation at reduced computational cost.

💡 Research Summary

The manuscript introduces a Dynamical Low‑Rank Ensemble Kalman Filter (DLR‑ENKF) designed for joint state‑parameter estimation in high‑dimensional dynamical systems. Traditional ensemble Kalman filters (EnKF) propagate each ensemble member in the full state space, which becomes computationally prohibitive when the underlying model originates from a fine discretisation of a PDE. The authors address this bottleneck by embedding a dynamical low‑rank (DLR) approximation directly into the filtering density. In the DLR framework the augmented state‑parameter vector (X=