Model Calibration and Parameter Estimation

1. Front Matter

   Pages i-xxviii

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2. Introduction

   • Ne-Zheng Sun, Alexander Sun

   Pages 1-24

3. The Classical Inverse Problem

   • Ne-Zheng Sun, Alexander Sun

   Pages 25-67

4. Multiobjective Inversion and Regularization

   • Ne-Zheng Sun, Alexander Sun

   Pages 69-105

5. Statistical Methods for Parameter Estimation

   • Ne-Zheng Sun, Alexander Sun

   Pages 107-139

6. Model Differentiation

   • Ne-Zheng Sun, Alexander Sun

   Pages 141-184

7. Model Dimension Reduction

   • Ne-Zheng Sun, Alexander Sun

   Pages 185-245

8. Model Structure Identification

   • Ne-Zheng Sun, Alexander Sun

   Pages 247-303

9. Development of Data-Driven Models

   • Ne-Zheng Sun, Alexander Sun

   Pages 305-359

10. Data Assimilation for Inversion

    • Ne-Zheng Sun, Alexander Sun

    Pages 361-406

11. Model Uncertainty Quantification

    • Ne-Zheng Sun, Alexander Sun

    Pages 407-458

12. Optimal Experimental Design

    • Ne-Zheng Sun, Alexander Sun

    Pages 459-507

13. Goal-Oriented Modeling

    • Ne-Zheng Sun, Alexander Sun

    Pages 509-551

14. Back Matter

    Pages 553-621

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This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making. For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling. Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems. Algorithms for mathematical tools used in this book, such as numerical optimization, automatic differentiation, adaptive parameterization, hierarchical Bayesian, metamodeling, Markov chain Monte Carlo, are covered in details. This book can be used as a reference for graduate and upper level undergraduate students majoring in environmental engineering, hydrology, and geosciences. It also serves as an essential reference book for professionals such as petroleum engineers, mining engineers, chemists, mechanical engineers, biologists, biology and medical engineering, applied mathematicians, and others who perform mathematical modeling.

• Forward Problems
• Inverse Problems
• Mathematical Modeling
• Model Calibration and Parameter Estimation
• Singluar Vector Decomposition
• hydrogeology

• Department of Civil and Environmental Engineering, University of California at Los Angeles, Los Angeles, USA

  Ne-Zheng Sun

• Bureau of Economics Geology, Jackson School of Geosciences, Univeristy of Texas at Austin, San Antonio, USA

  Alexander Sun

Ne-Zheng Sun, Adjunct Professor, Civil & Environmental Engineering Department, University of California at Los Angles, USA Alexander Y. Sun, Research Scientist, Bureau of Economic Geology, Jackson School of Geosciences, University of Texas at Austin, USA

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