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Parameter ESTimation With the Gauss-Levenberg-Marquardt Algorithm: An Intuitive Guide
Michael N Fienen1, Jeremy T White2, Mohamed Hayek3
1U.S. Geological Survey, Upper Midwest Water Science Center, Madison, Wisconsin.
Ground Water
|July 23, 2024
Summary
This paper reviews the Gauss-Levenberg-Marquardt (GLM) algorithm and its ensemble extension (iES). It offers insights into parameter estimation performance, tuning, and objective functions for tools like PEST.
Area of Science:
- Geosciences
- Computational Science
- Data Science
Background:
- Parameter estimation is crucial for model calibration.
- The Gauss-Levenberg-Marquardt (GLM) algorithm is a widely used optimization technique.
- Ensemble methods extend parameter estimation for complex models.
Purpose of the Study:
- To review the derivation and practical application of the GLM algorithm.
- To explore its extension for ensemble parameter estimation (iES).
- To provide insights into algorithm tuning and objective function construction for improved performance.
Main Methods:
- Review of the mathematical derivation of the GLM algorithm.
- Exploration of graphical methods for visualizing algorithm behavior.
- Analysis of tuning parameters and objective function construction in PEST and PEST++.
Main Results:
- Understanding the control of parameter trajectory and step size in GLM.
- Demonstration of how iES handles non-unique outcomes via objective function design.
- Insights into the impact of observation noise on iES performance.
Conclusions:
- GLM and iES offer robust approaches to parameter estimation.
- Careful tuning and objective function design are critical for successful model calibration.
- These insights benefit users of PEST, PEST++, and similar software.
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