Estimating the State of Large Spatiotemporally Chaotic Systems

TL;DR

This paper demonstrates a data assimilation method tailored for large, high-dimensional spatiotemporally chaotic systems, using Rayleigh-Benard convection as a case study, and extends it for parameter estimation.

Contribution

The paper introduces a novel data assimilation approach capable of handling high-dimensional chaotic systems and extends it to estimate unknown system parameters.

Findings

Method successfully applied to Rayleigh-Benard convection

Effective in estimating system states in high-dimensional chaos

Potential applicability to various spatiotemporally chaotic systems

Abstract

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the high dimensionality of large spatiotemporally chaotic systems prevents the use of classical data assimilation techniques. Here, via numerical computations on the paradigmatic example of large aspect ratio Rayleigh-Benard convection, we demonstrate the applicability of a recently developed data assimilation method designed to circumvent this difficulty. In addition, we describe extensions of the algorithm for estimating unknown system parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of situations in which there is spatiotemporally chaotic behavior.