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.
General
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