Basics and Trends in Sensitivity Analysis: Theory and Practice in R
Basics and Trends in Sensitivity Analysis: Theory and Practice in R

Author: Sébastien Da Veiga

Publisher: SIAM

Published: 2021-10-14

Total Pages: 307

ISBN-13: 1611976693

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This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol’ indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.

Decision and Prediction Analysis Powered With Operations Research
Decision and Prediction Analysis Powered With Operations Research

Author: Bubevski, Vojo

Publisher: IGI Global

Published: 2024-07-16

Total Pages: 298

ISBN-13:

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Organizations today face complex decisions and uncertainties that can have a profound impact on their financial stability and strategic direction. Traditional decision-making methods often fall short when it comes to addressing multifaceted issues like financing, product manufacturing, and facility location. These challenges demand a robust framework that quantifies factors, assesses risks, and provides optimal solutions. Without advanced tools and techniques, businesses are at risk of making uninformed decisions that could lead to significant financial losses and missed opportunities. The urgency to equip yourself with these tools is clear. Decision and Prediction Analysis Powered With Operations Research offers a comprehensive solution to these challenges. This book integrates operations research techniques to reframe and solve complex business problems. It provides a detailed exploration of decision analysis tools, such as influence diagrams and decision trees, which help visualize and assess various decision scenarios. By applying these tools, organizations can better understand uncertainties, evaluate risks, and make decisions that maximize expected utility and achieve strategic objectives.

Studies in Theoretical and Applied Statistics
Studies in Theoretical and Applied Statistics

Author: Nicola Salvati

Publisher: Springer Nature

Published: 2023-02-14

Total Pages: 548

ISBN-13: 3031166094

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This book includes a wide selection of papers presented at the 50th Scientific Meeting of the Italian Statistical Society (SIS2021), held virtually on 21-25 June 2021. It covers a wide variety of subjects ranging from methodological and theoretical contributions to applied works and case studies, giving an excellent overview of the interests of the Italian statisticians and their international collaborations. Intended for researchers interested in theoretical and empirical issues, this volume provides interesting starting points for further research.

Interpretability for Industry 4.0 : Statistical and Machine Learning Approaches
Interpretability for Industry 4.0 : Statistical and Machine Learning Approaches

Author: Antonio Lepore

Publisher: Springer Nature

Published: 2022-10-19

Total Pages: 130

ISBN-13: 3031124022

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This volume provides readers with a compact, stimulating and multifaceted introduction to interpretability, a key issue for developing insightful statistical and machine learning approaches as well as for communicating modelling results in business and industry. Different views in the context of Industry 4.0 are offered in connection with the concepts of explainability of machine learning tools, generalizability of model outputs and sensitivity analysis. Moreover, the book explores the integration of Artificial Intelligence and robust analysis of variance for big data mining and monitoring in Additive Manufacturing, and sheds new light on interpretability via random forests and flexible generalized additive models together with related software resources and real-world examples.

Uncertainty Analyses in Environmental Sciences and Hydrogeology
Uncertainty Analyses in Environmental Sciences and Hydrogeology

Author: Rachid Ababou

Publisher: Springer Nature

Published: 2024-01-21

Total Pages: 103

ISBN-13: 9819962412

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This book highlights several methods and quantitative implementations of both probabilistic and fuzzy-based approaches to uncertainty quantification and uncertainty propagation through environmental subsurface pollution models with uncertain input parameters. The book focuses on methods as well as applications in hydrogeology, soil hydrology, groundwater contamination, and related areas (e.g., corrosion of nuclear waste canisters). The methods are illustrated for a broad spectrum of models, from non-differential I/O models to complex PDE solvers, including a novel 3D quasi-analytical model of contaminant transport, and a site-specific computer model of dissolved contaminant migration from a DNAPL (Dense Non Aqueous Phase Liquid) pollution source.

Uncertainty Quantification
Uncertainty Quantification

Author: Ralph C. Smith

Publisher: SIAM

Published: 2024-09-13

Total Pages: 571

ISBN-13: 1611977843

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Uncertainty quantification serves a fundamental role when establishing the predictive capabilities of simulation models. This book provides a comprehensive and unified treatment of the mathematical, statistical, and computational theory and methods employed to quantify uncertainties associated with models from a wide range of applications. Expanded and reorganized, the second edition includes advances in the field and provides a comprehensive sensitivity analysis and uncertainty quantification framework for models from science and engineering. It contains new chapters on random field representations, observation models, parameter identifiability and influence, active subspace analysis, and statistical surrogate models, and a completely revised chapter on local sensitivity analysis. Other updates to the second edition are the inclusion of over 100 exercises and many new examples — several of which include data — and UQ Crimes listed throughout the text to identify common misconceptions and guide readers entering the field. Uncertainty Quantification: Theory, Implementation, and Applications, Second Edition is intended for advanced undergraduate and graduate students as well as researchers in mathematics, statistics, engineering, physical and biological sciences, operations research, and computer science. Readers are assumed to have a basic knowledge of probability, linear algebra, differential equations, and introductory numerical analysis. The book can be used as a primary text for a one-semester course on sensitivity analysis and uncertainty quantification or as a supplementary text for courses on surrogate and reduced-order model construction and parameter identifiability analysis.

Mathematical Theory of Finite Elements
Mathematical Theory of Finite Elements

Author: Leszek F. Demkowicz

Publisher: SIAM

Published: 2023-09-22

Total Pages: 217

ISBN-13: 1611977738

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This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.

Nonlocal Integral Equation Continuum Models
Nonlocal Integral Equation Continuum Models

Author: Marta D'Elia

Publisher: SIAM

Published: 2024-09-12

Total Pages: 187

ISBN-13: 161197805X

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The book presents the state of the art of nonlocal modeling and discretization and provides a practical introduction to nonlocal modeling for readers who are not familiar with such models. These models have recently become a viable alternative to classical partial differential equations when the latter are unable to capture effects such as discontinuities and multiscale behavior in a system of interest. Because of their integral nature, nonlocal operators allow for the relaxation of regularity requirements on the solution and thus allow for the capture of multiscale effects, the result of which is their successful use in many scientific and engineering applications. The book also provides a thorough analysis and numerical treatment of nonstandard nonlocal models, focusing on both well-known and nonstandard interaction neighborhoods. In addition, the book delivers an extensive practical treatment of the implementation of discretization strategies via finite element methods. Numerous figures are provided as concrete examples to illustrate both the analytic and computational results. Nonlocal Integral Equation Continuum Models: Nonstandard Interaction Neighborhoods and Finite Element Discretizations is intended for mathematical and application researchers interested in alternatives to using partial differential equation models that better describe the phenomena they are interested in. The book will also be of use to computational scientists and engineers who need to make sense of how to use available software, improve existing software, or develop new software tailored to their application interests.

Sparse Polynomial Approximation of High-Dimensional Functions
Sparse Polynomial Approximation of High-Dimensional Functions

Author: Ben Adcock

Publisher: SIAM

Published: 2022-02-16

Total Pages: 310

ISBN-13: 161197688X

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Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

Methods in Computational Science
Methods in Computational Science

Author: Johan Hoffman

Publisher: SIAM

Published: 2021-10-19

Total Pages: 425

ISBN-13: 1611976723

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Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory.