Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Wang, Yu, Hero, Alfred
Institution: University of Michigan
Language: English
Subfield: Atmospheric Science
Field: Earth and Planetary Sciences
Domain: Physical Sciences
Open Access status: green
Awards: G1083510804, G6457940185
OpenAlex ID: W4226055263