Multiway Ensemble Kalman Filter

2021/12/08 by Yu Wang, Wang, Yu, Alfred O. Hero +1
Earth and Planetary Sciences · Environmental Science · #Applications (stat.AP) #Climate variability and models #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Meteorological Phenomena and Simulations #Soil Geostatistics and Mapping

paper · pdf · doi:10.48550/arxiv.2112.04322

openalex publication_date 2021/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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