Modern scientific computational methods are undergoing a
transformative change; big data and statistical learning methods
now have the potential to outperform the classical first-principles
modeling paradigm. This book bridges this transition, connecting
the theory of probability, stochastic processes, functional
analysis, numerical analysis, and differential geometry. It
describes two classes of computational methods to leverage data for
modeling dynamical systems. The first is concerned with data
fitting algorithms to estimate parameters in parametric models that
are postulated on the basis of physical or dynamical laws. The
second is on operator estimation, which uses the data to
nonparametrically approximate the operator generated by the
transition function of the underlying dynamical systems. This
self-contained book is suitable for graduate studies in applied
mathematics, statistics, and engineering. Carefully chosen
elementary examples with supplementary MATLAB (R) codes and
appendices covering the relevant prerequisite materials are
provided, making it suitable for self-study.
General
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