Applied Artificial Neural Network Methods for Engineers and Scientists: Solving Algebraic Equations

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.

本書的目的是使用專家級的人工神經網絡（ANN）來處理科學和工程的不同應用問題。因此，本書從ANN的基礎知識開始，並介紹了與代數方程式相關的不同數學預備知識。然後，它介紹了基於ANN的方法來解決不同的代數方程式，如多項式方程式、丟番圖方程式、超越方程式、線性和非線性方程組、特徵值問題等，這些方程式是處理本書內容中提到的應用問題的基礎方程式。儘管存在各種處理這些問題的方法，但有時這些方法可能依賴於問題本身，並且可能無法給出特定離散化的收斂解。因此，本書介紹了基於ANN的方法來解決這些問題。書中包含了詳細的ANN架構、逐步過程和算法。通過不同的應用和數學問題解決了不同的示例問題。收斂圖和/或收斂表顯示了這些方法的有效性。值得一提的是，本書使用基於ANN的方法解決了各種應用問題，如麵包店問題、電力電子應用、極點配置、電力網絡分析、結構工程問題等。