{"title":"Parameter ESTimation With the Gauss–Levenberg–Marquardt Algorithm: An Intuitive Guide","authors":"Michael N. Fienen, Jeremy T. White, Mohamed Hayek","doi":"10.1111/gwat.13433","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":12866,"journal":{"name":"Groundwater","volume":"63 1","pages":"93-104"},"PeriodicalIF":2.0000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/gwat.13433","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groundwater","FirstCategoryId":"89","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/gwat.13433","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOSCIENCES, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Ground Water is the leading international journal focused exclusively on ground water. Since 1963, Ground Water has published a dynamic mix of papers on topics related to ground water including ground water flow and well hydraulics, hydrogeochemistry and contaminant hydrogeology, application of geophysics, groundwater management and policy, and history of ground water hydrology. This is the journal you can count on to bring you the practical applications in ground water hydrology.
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