Iterative ensemble smoother as an approximate solution to a regularized minimum-average-cost problem: theory and applications

TL;DR

This paper presents an alternative theoretical framework for the iterative ensemble smoother (iES) using a regularized Levenberg-Marquardt approach to solve a minimum-average-cost problem, enhancing understanding and performance in nonlinear applications.

Contribution

It introduces a new theoretical perspective on iES based on RLM, providing insights and practical guidelines for improved smoothing algorithms.

Findings

RLM-MAC algorithm performs comparably or better than traditional iES in numerical tests.

The approach offers improved performance in strongly nonlinear systems.

Provides theoretical analysis and practical comparisons across different applications.

Abstract

The focus of this work is on an alternative implementation of the iterative ensemble smoother (iES). We show that iteration formulae similar to those used in \cite{chen2013-levenberg,emerick2012ensemble} can be derived by adopting a regularized Levenberg-Marquardt (RLM) algorithm \cite{jin2010regularized} to approximately solve a minimum-average-cost (MAC) problem. This not only leads to an alternative theoretical tool in understanding and analyzing the behaviour of the aforementioned iES, but also provides insights and guidelines for further developments of the smoothing algorithms. For illustration, we compare the performance of an implementation of the RLM-MAC algorithm to that of the approximate iES used in \cite{chen2013-levenberg} in three numerical examples: an initial condition estimation problem in a strongly nonlinear system, a facies estimation problem in a 2D reservoir and the history matching problem in the Brugge field case. In these three specific cases, the RLM-MAC algorithm exhibits comparable or even better performance, especially in the strongly nonlinear system.