Multiway Ensemble Kalman Filter
Yu Wang, Alfred Hero

TL;DR
This paper investigates the integration of multiway covariance estimators into the ensemble Kalman filter to improve the accuracy and interpretability of physics-driven forecasting for PDE-governed dynamical processes.
Contribution
It introduces the use of multiway covariance and inverse covariance estimators within EnKF, demonstrating their effectiveness in tracking PDE-based systems.
Findings
Multiway estimators improve EnKF accuracy for PDE systems.
Certain estimators enhance interpretability of the covariance structure.
EnKF with multiway estimators effectively tracks Poisson and convection-diffusion PDEs.
Abstract
In this work, we study the emergence of sparsity and multiway structures in second-order statistical characterizations of dynamical processes governed by partial differential equations (PDEs). We consider several state-of-the-art multiway covariance and inverse covariance (precision) matrix estimators and examine their pros and cons in terms of accuracy and interpretability in the context of physics-driven forecasting when incorporated into the ensemble Kalman filter (EnKF). In particular, we show that multiway data generated from the Poisson and the convection-diffusion types of PDEs can be accurately tracked via EnKF when integrated with appropriate covariance and precision matrix estimators.
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Taxonomy
TopicsMeteorological Phenomena and Simulations · Climate variability and models · Soil Geostatistics and Mapping
