Multiway Ensemble Kalman Filter

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.