Multiway Ensemble Kalman Filter
This work addresses forecasting accuracy for physics-driven systems, but it appears incremental as it combines existing estimators with a known filter method.
The paper tackles the challenge of forecasting dynamical processes governed by PDEs by integrating multiway covariance and precision matrix estimators into the ensemble Kalman filter, showing accurate tracking for Poisson and convection-diffusion PDEs.
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.