Parameter ESTimation with the Gauss–Levenberg–Marquardt algorithm: An intuitive guide

Groundwater
By: , and 

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Abstract

In this paper, we review the derivation of the Gauss–Levenberg–Marquardt (GLM) algorithm and its extension to ensemble parameter estimation. We explore the use of graphical methods to provide insights into how the algorithm works in practice and discuss the implications of both algorithm tuning parameters and objective function construction in performance. Some insights include understanding the control of both parameter trajectory and step size for GLM as a function of tuning parameters. Furthermore, for the iterative Ensemble Smoother (iES), we discuss the importance of noise on observations and show how iES can cope with non-unique outcomes based on objective function construction. These insights are valuable for modelers using PEST, PEST++, or similar parameter estimation tools.

Publication type Article
Publication Subtype Journal Article
Title Parameter ESTimation with the Gauss–Levenberg–Marquardt algorithm: An intuitive guide
Series title Groundwater
DOI 10.1111/gwat.13433
Volume 63
Issue 1
Publication Date July 23, 2024
Year Published 2024
Language English
Publisher Wiley
Contributing office(s) Upper Midwest Water Science Center
Description 12 p.
First page 93
Last page 104
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