A Review of the EnKF for Parameter Estimation

TL;DR

This paper reviews the ensemble Kalman filter's application to inverse problems, focusing on ensemble Kalman Inversion (EKI) for parameter estimation in high-dimensional PDE-constrained problems, with insights into recent research and numerical experiments.

Contribution

It provides a comprehensive review of EKI methodology, highlighting recent developments and applications in geosciences and weather prediction.

Findings

EKI effectively estimates parameters in high-dimensional inverse problems.

Numerical experiments demonstrate EKI's applicability to geosciences models.

Emerging research areas include advanced EKI techniques and applications.

Abstract

The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance matrices. In this chapter we present a relatively recent topic which is the application of the EnKF to inverse problems, known as ensemble Kalman Inversion (EKI). EKI is used for parameter estimation, which can be viewed as a black-box optimizer for PDE-constrained inverse problems. We present in this chapter a review of the discussed methodology, while presenting emerging and new areas of research, where numerical experiments are provided on numerous interesting models arising in geosciences and numerical weather prediction.