Neural Networks And Numerical Analysis
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| Author | : A Browne |
| Publisher | : CRC Press |
| Total Pages | : 294 |
| Release | : 1997-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780750304993 |
Neural Network Analysis, Architectures and Applications discusses the main areas of neural networks, with each authoritative chapter covering the latest information from different perspectives. Divided into three parts, the book first lays the groundwork for understanding and simplifying networks. It then describes novel architectures and algorithms, including pulse-stream techniques, cellular neural networks, and multiversion neural computing. The book concludes by examining various neural network applications, such as neuron-fuzzy control systems and image compression. This final part of the book also provides a case study involving oil spill detection. This book is invaluable for students and practitioners who have a basic understanding of neural computing yet want to broaden and deepen their knowledge of the field.
| Author | : Bruno Després |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 177 |
| Release | : 2022-08-22 |
| Genre | : Mathematics |
| ISBN | : 3110783266 |
This book uses numerical analysis as the main tool to investigate methods in machine learning and neural networks. The efficiency of neural network representations for general functions and for polynomial functions is studied in detail, together with an original description of the Latin hypercube method and of the ADAM algorithm for training. Furthermore, unique features include the use of Tensorflow for implementation session, and the description of on going research about the construction of new optimized numerical schemes.
| Author | : Snehashish Chakraverty |
| Publisher | : World Scientific |
| Total Pages | : 192 |
| Release | : 2021-01-26 |
| Genre | : Computers |
| ISBN | : 9811230226 |
The aim of this book is to handle different application problems of science and engineering using expert Artificial Neural Network (ANN). As such, the book starts with basics of ANN along with different mathematical preliminaries with respect to algebraic equations. Then it addresses ANN based methods for solving different algebraic equations viz. polynomial equations, diophantine equations, transcendental equations, system of linear and nonlinear equations, eigenvalue problems etc. which are the basic equations to handle the application problems mentioned in the content of the book. Although there exist various methods to handle these problems, but sometimes those may be problem dependent and may fail to give a converge solution with particular discretization. Accordingly, ANN based methods have been addressed here to solve these problems. Detail ANN architecture with step by step procedure and algorithm have been included. Different example problems are solved with respect to various application and mathematical problems. Convergence plots and/or convergence tables of the solutions are depicted to show the efficacy of these methods. It is worth mentioning that various application problems viz. Bakery problem, Power electronics applications, Pole placement, Electrical Network Analysis, Structural engineering problem etc. have been solved using the ANN based methods.
| Author | : Herbert K. H. Lee |
| Publisher | : SIAM |
| Total Pages | : 106 |
| Release | : 2004-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898718423 |
Bayesian Nonparametrics via Neural Networks is the first book to focus on neural networks in the context of nonparametric regression and classification, working within the Bayesian paradigm. Its goal is to demystify neural networks, putting them firmly in a statistical context rather than treating them as a black box. This approach is in contrast to existing books, which tend to treat neural networks as a machine learning algorithm instead of a statistical model. Once this underlying statistical model is recognized, other standard statistical techniques can be applied to improve the model. The Bayesian approach allows better accounting for uncertainty. This book covers uncertainty in model choice and methods to deal with this issue, exploring a number of ideas from statistics and machine learning. A detailed discussion on the choice of prior and new noninformative priors is included, along with a substantial literature review. Written for statisticians using statistical terminology, Bayesian Nonparametrics via Neural Networks will lead statisticians to an increased understanding of the neural network model and its applicability to real-world problems.
| Author | : Genki Yagawa |
| Publisher | : Springer Nature |
| Total Pages | : 233 |
| Release | : 2021-02-26 |
| Genre | : Technology & Engineering |
| ISBN | : 3030661113 |
This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.
| Author | : S. Chakraverty |
| Publisher | : CRC Press |
| Total Pages | : 157 |
| Release | : 2017-07-20 |
| Genre | : Mathematics |
| ISBN | : 1351651315 |
Differential equations play a vital role in the fields of engineering and science. Problems in engineering and science can be modeled using ordinary or partial differential equations. Analytical solutions of differential equations may not be obtained easily, so numerical methods have been developed to handle them. Machine intelligence methods, such as Artificial Neural Networks (ANN), are being used to solve differential equations, and these methods are presented in Artificial Neural Networks for Engineers and Scientists: Solving Ordinary Differential Equations. This book shows how computation of differential equation becomes faster once the ANN model is properly developed and applied.
| Author | : Martin Anthony |
| Publisher | : SIAM |
| Total Pages | : 137 |
| Release | : 2001-01-01 |
| Genre | : Computers |
| ISBN | : 089871480X |
This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.
| Author | : Neha Yadav |
| Publisher | : Springer |
| Total Pages | : 124 |
| Release | : 2015-02-26 |
| Genre | : Mathematics |
| ISBN | : 9401798168 |
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 | : Raul Rojas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 511 |
| Release | : 2013-06-29 |
| Genre | : Computers |
| ISBN | : 3642610684 |
Neural networks are a computing paradigm that is finding increasing attention among computer scientists. In this book, theoretical laws and models previously scattered in the literature are brought together into a general theory of artificial neural nets. Always with a view to biology and starting with the simplest nets, it is shown how the properties of models change when more general computing elements and net topologies are introduced. Each chapter contains examples, numerous illustrations, and a bibliography. The book is aimed at readers who seek an overview of the field or who wish to deepen their knowledge. It is suitable as a basis for university courses in neurocomputing.
| Author | : Justin Solomon |
| Publisher | : CRC Press |
| Total Pages | : 400 |
| Release | : 2015-06-24 |
| Genre | : Computers |
| ISBN | : 1482251892 |
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
