Parameter ESTimation With the Gauss–Levenberg–Marquardt Algorithm: An Intuitive Guide

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 para...

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Bibliographic Details
Published in:Ground water Vol. 63; no. 1; pp. 93 - 104
Main Authors: Fienen, Michael N., White, Jeremy T., Hayek, Mohamed
Format: Journal Article
Language:English
Published: Malden, US Blackwell Publishing Ltd 01.01.2025
Ground Water Publishing Company
Subjects:
Algorithms
Construction
exhibitions
Graphical methods
Groundwater
Models, Theoretical
Objective function
objectives
Parameter estimation
Parameters
Pests
Tuning
ISSN:0017-467X, 1745-6584, 1745-6584
Online Access:Get full text
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Summary: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.  
Bibliography:The authors do not have any conflicts of interest or financial disclosures to report.
We break down the mathematics underlying the PEST/PEST++ parameter estimation tools with graphical interpretations to provide insights.
Article impact statement
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SourceType-Scholarly Journals-1
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ISSN:0017-467X
1745-6584
1745-6584
DOI:10.1111/gwat.13433