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.
