Download or read book Sparse Polynomial Approximation of High Dimensional Functions written by Ben Adcock and published by SIAM. This book was released on 2022-02-16 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book High Dimensional Optimization and Probability written by Ashkan Nikeghbali and published by Springer Nature. This book was released on 2022-08-04 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces. The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas. Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Download or read book Sparse Polynomial Approximation of High Dimensional Functions written by Ben Adcock and published by Society for Industrial and Applied Mathematics (SIAM). This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a book about polynomial approximation in high dimensions"--

Download or read book Numerical Analysis meets Machine Learning written by and published by Elsevier. This book was released on 2024-06-13 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Analysis Meets Machine Learning series, highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on the Numerical Analysis Meets Machine Learning

Download or read book Compressed Sensing and its Applications written by Holger Boche and published by Birkhäuser. This book was released on 2018-01-17 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing. Article authors address their techniques for solving the problems of compressed sensing, as well as connections to related areas like detecting community-like structures in graphs, curbatures on Grassmanians, and randomized tensor train singular value decompositions. Some of the novel applications covered include dimensionality reduction, information theory, random matrices, sparse approximation, and sparse recovery. This book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering, as well as other applied scientists exploring the potential applications for the novel methodology of compressed sensing. An introduction to the subject of compressed sensing is also provided for researchers interested in the field who are not as familiar with it.

Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 written by Spencer J. Sherwin and published by Springer Nature. This book was released on 2020-08-11 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

Download or read book Compressive Imaging Structure Sampling Learning written by Ben Adcock and published by Cambridge University Press. This book was released on 2021-09-16 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate, robust and fast image reconstruction is a critical task in many scientific, industrial and medical applications. Over the last decade, image reconstruction has been revolutionized by the rise of compressive imaging. It has fundamentally changed the way modern image reconstruction is performed. This in-depth treatment of the subject commences with a practical introduction to compressive imaging, supplemented with examples and downloadable code, intended for readers without extensive background in the subject. Next, it introduces core topics in compressive imaging – including compressed sensing, wavelets and optimization – in a concise yet rigorous way, before providing a detailed treatment of the mathematics of compressive imaging. The final part is devoted to recent trends in compressive imaging: deep learning and neural networks. With an eye to the next decade of imaging research, and using both empirical and mathematical insights, it examines the potential benefits and the pitfalls of these latest approaches.

Download or read book Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics written by Gianluigi Rozza and published by SIAM. This book was released on 2022-11-21 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications. This book will be of interest to researchers and graduate students in the field of reduced order modeling.

Download or read book Mathematical Theory of Finite Elements written by Leszek F. Demkowicz and published by SIAM. This book was released on 2023-09-22 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Ramble Through Probability written by Samopriya Basu and published by SIAM. This book was released on 2024-03-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is difficult to overstate their importance in the quantitative disciplines. This book traces an eclectic path through the fundamentals of the topic to make the material accessible to a broad range of students. A Ramble through Probability: How I Learned to Stop Worrying and Love Measure Theory brings together the key elements and applications in a unified presentation aimed at developing intuition; contains an extensive collection of examples that illustrate, explain, and apply the theories; and is supplemented with videos containing commentary and explanations of select proofs on an ancillary website. This book is intended for graduate students in engineering, mathematics, science, and statistics. Researchers who need to use probability theory will also find it useful. It is appropriate for graduate-level courses on measure theory and/or probability theory.

Download or read book Quantification of Uncertainty Improving Efficiency and Technology written by Marta D'Elia and published by Springer Nature. This book was released on 2020-07-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores four guiding themes – reduced order modelling, high dimensional problems, efficient algorithms, and applications – by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the book’s content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.

Download or read book Sparse Grids and Applications Stuttgart 2014 written by Jochen Garcke and published by Springer. This book was released on 2016-03-16 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of LNCSE is a collection of the papers from the proceedings of the third workshop on sparse grids and applications. Sparse grids are a popular approach for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different guises, are frequently the method of choice, be it spatially adaptive in the hierarchical basis or via the dimensionally adaptive combination technique. Demonstrating once again the importance of this numerical discretization scheme, the selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures. The book also discusses a range of applications, including uncertainty quantification and plasma physics.

Download or read book Safety Reliability Risk and Life Cycle Performance of Structures and Infrastructures written by George Deodatis and published by CRC Press. This book was released on 2014-02-10 with total page 1112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures contains the plenary lectures and papers presented at the 11th International Conference on STRUCTURAL SAFETY AND RELIABILITY (ICOSSAR2013, New York, NY, USA, 16-20 June 2013), and covers major aspects of safety, reliability, risk and life-cycle performance of str

Download or read book Self Organization Computational Maps and Motor Control written by P.G. Morasso and published by Elsevier. This book was released on 1997-03-19 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of the computational structure of biological/robotic sensorimotor systems, distributed models have gained center stage in recent years, with a range of issues including self-organization, non-linear dynamics, field computing etc. This multidisciplinary research area is addressed here by a multidisciplinary team of contributors, who provide a balanced set of articulated presentations which include reviews, computational models, simulation studies, psychophysical, and neurophysiological experiments. The book is divided into three parts, each characterized by a slightly different focus: in part I, the major theme concerns computational maps which typically model cortical areas, according to a view of the sensorimotor cortex as "geometric engine" and the site of "internal models" of external spaces. Part II also addresses problems of self-organization and field computing, but in a simpler computational architecture which, although lacking a specialized cortical machinery, can still behave in a very adaptive and surprising way by exploiting the interaction with the real world. Finally part III is focused on the motor control issues related to the physical properties of muscular actuators and the dynamic interactions with the world. The reader will find different approaches on controversial issues, such as the role and nature of force fields, the need for internal representations, the nature of invariant commands, the vexing question about coordinate transformations, the distinction between hierachiacal and bi-directional modelling, and the influence of muscle stiffness.

Download or read book Hydro Environmental Analysis written by James L. Martin and published by CRC Press. This book was released on 2013-12-04 with total page 5742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on fundamental principles, Hydro-Environmental Analysis: Freshwater Environments presents in-depth information about freshwater environments and how they are influenced by regulation. It provides a holistic approach, exploring the factors that impact water quality and quantity, and the regulations, policy and management methods that are necessary to maintain this vital resource. It offers a historical viewpoint as well as an overview and foundation of the physical, chemical, and biological characteristics affecting the management of freshwater environments. The book concentrates on broad and general concepts, providing an interdisciplinary foundation. The author covers the methods of measurement and classification; chemical, physical, and biological characteristics; indicators of ecological health; and management and restoration. He also considers common indicators of environmental health; characteristics and operations of regulatory control structures; applicable laws and regulations; and restoration methods. The text delves into rivers and streams in the first half and lakes and reservoirs in the second half. Each section centers on the characteristics of those systems and methods of classification, and then moves on to discuss the physical, chemical, and biological characteristics of each. In the section on lakes and reservoirs, it examines the characteristics and operations of regulatory structures, and presents the methods commonly used to assess the environmental health or integrity of these water bodies. It also introduces considerations for restoration, and presents two unique aquatic environments: wetlands and reservoir tailwaters. Written from an engineering perspective, the book is an ideal introduction to the aquatic and limnological sciences for students of environmental science, as well as students of environmental engineering. It also serves as a reference for engineers and scientists involved in the management, regulation, or restoration of freshwater environments.

Download or read book Optimization and Control for Partial Differential Equations written by Roland Herzog and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-07 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.