Parameter Estimation and Inverse Problems

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Parameter Estimation and Inverse Problems,

Edition 4

Editors: By Richard C. Aster, Clifford H. Thurber and Brian Borchers

Publication Date: 01 May 2027

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The fourth edition of Parameter Estimation and Inverse Problems offers a comprehensive, accessible introduction to the fundamental techniques used in geophysical and scientific modeling. Building on previous editions, this volume covers a wide range of topics, including linear regression, regularization, nonlinear inverse problems, Bayesian methods, and machine learning applications. Notable updates include expanded discussions on Markov Chain Monte Carlo sampling, a new chapter dedicated to machine learning techniques, covering neural networks, physics-informed neural networks, and their applications in predictive modeling and inverse problems—and revised MATLAB and Python code archives to facilitate practical implementation. These updates ensure the text remains relevant for modern research and application. The chapters are organized to facilitate a logical progression, starting with foundational concepts such as classification, discretization, and regularization techniques. It then advances through iterative methods, sparsity, Fourier techniques, and nonlinear problems, providing a solid grounding in classical inverse problem approaches. The later sections introduce Bayesian methods, including Markov Chain Monte Carlo (MCMC) and gradient-based sampling techniques like Langevin Monte Carlo, to address uncertainty quantification. A new chapter on machine learning is positioned toward the end, offering an overview of neural networks and physics-informed neural networks for both predictive modeling and inverse problems. The epilogue synthesizes key insights and future directions, offering a cohesive perspective on the field’s ongoing evolution. This edition is particularly valuable for graduate students and researchers in geophysics, earth sciences, and engineering disciplines who seek a rigorous yet practical guide to inverse problem methodologies. It emphasizes current computational strategies and incorporates recent advances to ensure relevance in a rapidly evolving field. The book’s clear explanations, extensive exercises, and online code archives make it an essential resource for mastering inverse problems and parameter estimation, supporting both academic research and applied problem-solving in scientific and engineering contexts.

Key Features

Provides updated coverage of parameter estimation, inverse problems, Bayesian methods, and machine learning in geophysics
Serves as an accessible resource on MATLAB and Python, with revised code and new examples
Adds a chapter on machine learning’s evolving role in inverse problems
Expands MCMC discussions with more efficient sampling methods
Includes a "box" on inversion techniques for large seismic datasets
Features new questions, examples, and exercises to reinforce modern inverse problem techniques

About the author

By Richard C. Aster, Earth Scientist, New Mexico Institute of Mining and Technology, Socorro, USA; Clifford H. Thurber, University of Wisconsin-Madison, USA and Brian Borchers, New Mexico Institute of Mining and Technology, Socorro, USA

1. Introduction
2. Linear Regression
3. Rank Deficiency and Ill–Conditioning
4. Tikhonov Regularization
5. Discretizing Inverse Problems Using Basis Functions
6. Iterative Methods
7. Sparsity Regularization and Total Variation Techniques
8. Fourier Techniques
9. Nonlinear Regression
10. Nonlinear Inverse Problems
11. Bayesian Methods
12. Machine Learning from a Parameter Estimation and Inverse Problems Perspective
13. Epilogue Appendices

Parameter Estimation and Inverse Problems,

Editors: By Richard C. Aster, Clifford H. Thurber and Brian Borchers

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