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Books > Science & Mathematics > Mathematics > Probability & statistics
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Uncertainty Quantification and Predictive Computational Science - A Foundation for Physical Scientists and Engineers (Hardcover, 1st ed. 2018)
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Uncertainty Quantification and Predictive Computational Science - A Foundation for Physical Scientists and Engineers (Hardcover, 1st ed. 2018)
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This textbook teaches the essential background and skills for
understanding and quantifying uncertainties in a computational
simulation, and for predicting the behavior of a system under those
uncertainties. It addresses a critical knowledge gap in the
widespread adoption of simulation in high-consequence
decision-making throughout the engineering and physical sciences.
Constructing sophisticated techniques for prediction from basic
building blocks, the book first reviews the fundamentals that
underpin later topics of the book including probability, sampling,
and Bayesian statistics. Part II focuses on applying Local
Sensitivity Analysis to apportion uncertainty in the model outputs
to sources of uncertainty in its inputs. Part III demonstrates
techniques for quantifying the impact of parametric uncertainties
on a problem, specifically how input uncertainties affect outputs.
The final section covers techniques for applying uncertainty
quantification to make predictions under uncertainty, including
treatment of epistemic uncertainties. It presents the theory and
practice of predicting the behavior of a system based on the
aggregation of data from simulation, theory, and experiment. The
text focuses on simulations based on the solution of systems of
partial differential equations and includes in-depth coverage of
Monte Carlo methods, basic design of computer experiments, as well
as regularized statistical techniques. Code references, in python,
appear throughout the text and online as executable code, enabling
readers to perform the analysis under discussion. Worked examples
from realistic, model problems help readers understand the
mechanics of applying the methods. Each chapter ends with several
assignable problems. Uncertainty Quantification and Predictive
Computational Science fills the growing need for a classroom text
for senior undergraduate and early-career graduate students in the
engineering and physical sciences and supports independent study by
researchers and professionals who must include uncertainty
quantification and predictive science in the simulations they
develop and/or perform.
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