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Author : Monica C. Jackson
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (875 download)
Download or read book A Neural Network Approach to Variational Problems written by Monica C. Jackson and published by . This book was released on 1994 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sourav Banerjee
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659166860
Total Pages : 228 pages
Book Rating : 4.1/5 (668 download)
Download or read book Neural Networks for Variational Problems in Engineering written by Sourav Banerjee and published by LAP Lambert Academic Publishing. This book was released on 2012-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems arising in science and engineering aim to find a function which is the optimal value of a specified functional. Some examples include optimal control, inverse analysis and optimal shape design. Only some of these, regarded as variational problems, can be solved analytically, and the only general technique is to approximate the solution using direct methods. Unfortunately, variational problems are very difficult to solve, and it becomes necessary to innovate in the field of numerical methods in order to overcome the difficulties. The objective of this PhD Thesis is to develop a conceptual theory of neural networks from the perspective of functional analysis and variational calculus. Within this formulation, learning means to solve a variational problem by minimizing an objective functional associated to the neural network. The choice of the objective functional depends on the particular application. On the other side, its evaluation might need the integration of functions, ordinary differential equations or partial differential equations. As it will be shown, neural networks are able to deal with a wide range of applications in mathematics and physics.
Author : Roberto López González
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (84 download)
Download or read book Neural Networks for Variational Problems in Engineering written by Roberto López González and published by . This book was released on 2008 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lucas Pinheiro Cinelli
Publisher : Springer Nature
ISBN 13 : 3030706796
Total Pages : 173 pages
Book Rating : 4.0/5 (37 download)
Download or read book Variational Methods for Machine Learning with Applications to Deep Networks written by Lucas Pinheiro Cinelli and published by Springer Nature. This book was released on 2021-05-10 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a straightforward look at the concepts, algorithms and advantages of Bayesian Deep Learning and Deep Generative Models. Starting from the model-based approach to Machine Learning, the authors motivate Probabilistic Graphical Models and show how Bayesian inference naturally lends itself to this framework. The authors present detailed explanations of the main modern algorithms on variational approximations for Bayesian inference in neural networks. Each algorithm of this selected set develops a distinct aspect of the theory. The book builds from the ground-up well-known deep generative models, such as Variational Autoencoder and subsequent theoretical developments. By also exposing the main issues of the algorithms together with different methods to mitigate such issues, the book supplies the necessary knowledge on generative models for the reader to handle a wide range of data types: sequential or not, continuous or not, labelled or not. The book is self-contained, promptly covering all necessary theory so that the reader does not have to search for additional information elsewhere. Offers a concise self-contained resource, covering the basic concepts to the algorithms for Bayesian Deep Learning; Presents Statistical Inference concepts, offering a set of elucidative examples, practical aspects, and pseudo-codes; Every chapter includes hands-on examples and exercises and a website features lecture slides, additional examples, and other support material.
Author : Bilal M. Ayyub
Publisher : Springer Science & Business Media
ISBN 13 : 146155473X
Total Pages : 376 pages
Book Rating : 4.4/5 (615 download)
Download or read book Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach written by Bilal M. Ayyub and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty has been of concern to engineers, managers and . scientists for many centuries. In management sciences there have existed definitions of uncertainty in a rather narrow sense since the beginning of this century. In engineering and uncertainty has for a long time been considered as in sciences, however, synonymous with random, stochastic, statistic, or probabilistic. Only since the early sixties views on uncertainty have ~ecome more heterogeneous and more tools to model uncertainty than statistics have been proposed by several scientists. The problem of modeling uncertainty adequately has become more important the more complex systems have become, the faster the scientific and engineering world develops, and the more important, but also more difficult, forecasting of future states of systems have become. The first question one should probably ask is whether uncertainty is a phenomenon, a feature of real world systems, a state of mind or a label for a situation in which a human being wants to make statements about phenomena, i. e. , reality, models, and theories, respectively. One cart also ask whether uncertainty is an objective fact or just a subjective impression which is closely related to individual persons. Whether uncertainty is an objective feature of physical real systems seems to be a philosophical question. This shall not be answered in this volume.
Author : Rahul Parhi (Ph.D.)
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (138 download)
Download or read book On Ridge Splines, Neural Networks, and Variational Problems in Radon-domain BV Spaces written by Rahul Parhi (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep neural networks are not well understood mathematically and their success in many science and engineering applications is usually only backed by empirical evidence. In this dissertation, we study neural networks from first principles, beginning with the simplest architecture of shallow feedforward neural networks. We use tools from variational spline theory to mathematically understand neural networks. In particular, we view neural networks as a type of spline. We propose and study a new family of Banach spaces, which are bounded variation (BV) spaces defined via the Radon transform. These are the "native spaces" for neural networks. We show that finite-width neural networks are solutions to data-fitting variational problems over these spaces. Moreover, these variational problems can be recast as finite-dimensional neural network training problems with regularization schemes related to weight decay and path-norm regularization, giving theoretical insight into these common regularization schemes as well as providing several new, principled forms of regularization for (deep) neural networks. The Radon-domain BV spaces are also interesting from the perspective of functional analysis and statistical estimation. The best approximation and estimation error rates of these spaces are (essentially) independent of the input dimension, while the best linear approximation and estimation error rates suffer the curse of dimensionality. The Radon-domain BV spaces contain functions that are very smooth in all directions except (perhaps) a few directions. The anisotropic nature of these spaces distinguishes them from classical function spaces. This dissertation provides a first step towards a mathematical theory of neural networks through the lens of spline theory and functional analysis.
Author : Neha Yadav
Publisher : Springer
ISBN 13 : 9401798168
Total Pages : 124 pages
Book Rating : 4.4/5 (17 download)
Download or read book An Introduction to Neural Network Methods for Differential Equations written by Neha Yadav and published by Springer. This book was released on 2015-02-26 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.
Author : Wen Yu
Publisher : Springer
ISBN 13 : 3642015131
Total Pages : 1278 pages
Book Rating : 4.6/5 (42 download)
Download or read book Advances in Neural Networks - ISNN 2009 written by Wen Yu and published by Springer. This book was released on 2009-05-21 with total page 1278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book and its companion volumes, LNCS vols. 5551, 5552 and 5553, constitute the proceedings of the 6th International Symposium on Neural Networks (ISNN 2009), held during May 26–29, 2009 in Wuhan, China. Over the past few years, ISNN has matured into a well-established premier international symposium on neural n- works and related fields, with a successful sequence of ISNN symposia held in Dalian (2004), Chongqing (2005), Chengdu (2006), Nanjing (2007), and Beijing (2008). Following the tradition of the ISNN series, ISNN 2009 provided a high-level inter- tional forum for scientists, engineers, and educators to present state-of-the-art research in neural networks and related fields, and also to discuss with international colleagues on the major opportunities and challenges for future neural network research. Over the past decades, the neural network community has witnessed tremendous - forts and developments in all aspects of neural network research, including theoretical foundations, architectures and network organizations, modeling and simulation, - pirical study, as well as a wide range of applications across different domains. The recent developments of science and technology, including neuroscience, computer science, cognitive science, nano-technologies and engineering design, among others, have provided significant new understandings and technological solutions to move the neural network research toward the development of complex, large-scale, and n- worked brain-like intelligent systems. This long-term goal can only be achieved with the continuous efforts of the community to seriously investigate different issues of the neural networks and related fields.
Author : Oliver Nelles
Publisher : Springer Science & Business Media
ISBN 13 : 3662043238
Total Pages : 785 pages
Book Rating : 4.6/5 (62 download)
Download or read book Nonlinear System Identification written by Oliver Nelles and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written from an engineering point of view, this book covers the most common and important approaches for the identification of nonlinear static and dynamic systems. The book also provides the reader with the necessary background on optimization techniques, making it fully self-contained. The new edition includes exercises.
Author : Antonio Luciano Martire
Publisher : Roma TrE-Press
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.2/5 (597 download)
Download or read book Fractional Volterra Integral Equations: A Neural Network Approach written by Antonio Luciano Martire and published by Roma TrE-Press. This book was released on 2022-12-24 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Il Calcolo Frazionario ha recentemente guadagnato un crescente interesse nella letteratura economica e finanziaria. Per quanto riguarda i modelli economici, quelli di crescita sono stati modellati utilizzando una rappresentazione tramite derivate frazionarie. Questo tipo di equazioni non consente soluzioni in forma chiusa e quindi è necessario ricorrere a metodi numerici appropriati per ottenere approssimazioni accurate delle soluzioni. Per questo motivo, in questo contributo, proponiamo un approccio basato sulle cosiddette Physics Informed Neural Network per risolvere le equazioni integrali di Volterra di ordine frazionario. Alcuni esperimenti numerici mostrano l’accuratezza dell’algoritmo suggerito.
Author : Ke Chen
Publisher : Springer Nature
ISBN 13 : 3030986616
Total Pages : 1981 pages
Book Rating : 4.0/5 (39 download)
Download or read book Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging written by Ke Chen and published by Springer Nature. This book was released on 2023-02-24 with total page 1981 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.
Author : Panagiotis D. Panagiotopoulos
Publisher : Springer Science & Business Media
ISBN 13 : 3642516777
Total Pages : 453 pages
Book Rating : 4.6/5 (425 download)
Download or read book Hemivariational Inequalities written by Panagiotis D. Panagiotopoulos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.
Author : Andrey A. Radionov
Publisher : Springer Nature
ISBN 13 : 3031381262
Total Pages : 849 pages
Book Rating : 4.0/5 (313 download)
Download or read book Proceedings of the 9th International Conference on Industrial Engineering written by Andrey A. Radionov and published by Springer Nature. This book was released on 2023-08-28 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights recent findings in industrial, manufacturing and mechanical engineering and provides an overview of the state of the art in these fields, mainly in Russia and Eastern Europe. A broad range of topics and issues in modern engineering is discussed, including the machinery and mechanism design, dynamics of machines and working processes, friction, wear and lubrication in machines, design and manufacturing engineering of industrial facilities, transport and technological machines, mechanical treatment of materials, industrial hydraulic systems. This book gathers selected papers presented at the 9th International Conference on Industrial Engineering (ICIE), held in Sochi, Russia, in May 2023. The authors are experts in various fields of engineering, and all papers have been carefully reviewed. Given its scope, this book will be of interest to a wide readership, including mechanical and production engineers, lecturers in engineering disciplines, and engineering graduates.
Author : Svetozar D. Margenov
Publisher : Springer
ISBN 13 : 3540453466
Total Pages : 500 pages
Book Rating : 4.5/5 (44 download)
Download or read book Large-Scale Scientific Computing written by Svetozar D. Margenov and published by Springer. This book was released on 2003-06-30 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Large-Scale Scientific Computing, LSSC 2001, held in Sozopol, Bulgaria, in June 2001. The 7 invited full papers and 45 selected revised papers were carefully reviewed for inclusion in the book. The papers are organized in topical sections on robust preconditioning algorithms, Monte-Carlo methods, advanced programming environments for scientific computing, large-scale computations in air pollution modeling, large-scale computations in mechanical engineering, and numerical methods for incompressible flow.
Author : Joachim Gwinner
Publisher : CRC Press
ISBN 13 : 1351857673
Total Pages : 405 pages
Book Rating : 4.3/5 (518 download)
Download or read book Uncertainty Quantification in Variational Inequalities written by Joachim Gwinner and published by CRC Press. This book was released on 2021-12-24 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature
Author :
Publisher : Elsevier
ISBN 13 : 0443239851
Total Pages : 590 pages
Book Rating : 4.4/5 (432 download)
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
Author : Stefanos Kollias
Publisher : Springer
ISBN 13 : 3540386270
Total Pages : 1041 pages
Book Rating : 4.5/5 (43 download)
Download or read book Artificial Neural Networks - ICANN 2006 written by Stefanos Kollias and published by Springer. This book was released on 2006-09-01 with total page 1041 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 4131 and LNCS 4132 constitutes the refereed proceedings of the 16th International Conference on Artificial Neural Networks, ICANN 2006. The set presents 208 revised full papers, carefully reviewed and selected from 475 submissions. This first volume presents 103 papers, organized in topical sections on feature selection and dimension reduction for regression, learning algorithms, advances in neural network learning methods, ensemble learning, hybrid architectures, and more.
