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An Introduction to Neural Network Methods for Differential Equations

2015-02-26 Mathematics
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Release : 2015-02-26
Genre : Mathematics
Kind : eBook
Book Rating : 168/5 ( reviews)

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Book Synopsis An Introduction to Neural Network Methods for Differential Equations by : Neha Yadav

Download or read book An Introduction to Neural Network Methods for Differential Equations written by Neha Yadav. This book was released on 2015-02-26. 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.

Artificial Neural Networks for Engineers and Scientists

2017-07-20 Mathematics
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Release : 2017-07-20
Genre : Mathematics
Kind : eBook
Book Rating : 315/5 ( reviews)

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Book Synopsis Artificial Neural Networks for Engineers and Scientists by : S. Chakraverty

Download or read book Artificial Neural Networks for Engineers and Scientists written by S. Chakraverty. This book was released on 2017-07-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Semi-empirical Neural Network Modeling and Digital Twins Development

2019-11-23 Science
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Release : 2019-11-23
Genre : Science
Kind : eBook
Book Rating : 52X/5 ( reviews)

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Book Synopsis Semi-empirical Neural Network Modeling and Digital Twins Development by : Dmitriy Tarkhov

Download or read book Semi-empirical Neural Network Modeling and Digital Twins Development written by Dmitriy Tarkhov. This book was released on 2019-11-23. Available in PDF, EPUB and Kindle. Book excerpt: Semi-empirical Neural Network Modeling presents a new approach on how to quickly construct an accurate, multilayered neural network solution of differential equations. Current neural network methods have significant disadvantages, including a lengthy learning process and single-layered neural networks built on the finite element method (FEM). The strength of the new method presented in this book is the automatic inclusion of task parameters in the final solution formula, which eliminates the need for repeated problem-solving. This is especially important for constructing individual models with unique features. The book illustrates key concepts through a large number of specific problems, both hypothetical models and practical interest. - Offers a new approach to neural networks using a unified simulation model at all stages of design and operation - Illustrates this new approach with numerous concrete examples throughout the book - Presents the methodology in separate and clearly-defined stages

Applied Artificial Neural Network Methods For Engineers And Scientists: Solving Algebraic Equations

2021-01-26 Computers
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Release : 2021-01-26
Genre : Computers
Kind : eBook
Book Rating : 226/5 ( reviews)

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Book Synopsis Applied Artificial Neural Network Methods For Engineers And Scientists: Solving Algebraic Equations by : Snehashish Chakraverty

Download or read book Applied Artificial Neural Network Methods For Engineers And Scientists: Solving Algebraic Equations written by Snehashish Chakraverty. This book was released on 2021-01-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Deep Learning in Computational Mechanics

2021-08-05 Technology & Engineering
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Release : 2021-08-05
Genre : Technology & Engineering
Kind : eBook
Book Rating : 873/5 ( reviews)

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Book Synopsis Deep Learning in Computational Mechanics by : Stefan Kollmannsberger

Download or read book Deep Learning in Computational Mechanics written by Stefan Kollmannsberger. This book was released on 2021-08-05. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a first course on deep learning in computational mechanics. The book starts with a short introduction to machine learning’s fundamental concepts before neural networks are explained thoroughly. It then provides an overview of current topics in physics and engineering, setting the stage for the book’s main topics: physics-informed neural networks and the deep energy method. The idea of the book is to provide the basic concepts in a mathematically sound manner and yet to stay as simple as possible. To achieve this goal, mostly one-dimensional examples are investigated, such as approximating functions by neural networks or the simulation of the temperature’s evolution in a one-dimensional bar. Each chapter contains examples and exercises which are either solved analytically or in PyTorch, an open-source machine learning framework for python.

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