Design and analysis of new complex zeroing neural network for a set of dynamic complex linear equations

2019 ◽  
Vol 363 ◽  
pp. 171-181 ◽  
Author(s):  
Lin Xiao ◽  
Qian Yi ◽  
Jianhua Dai ◽  
Kenli Li ◽  
Zeshan Hu
Keyword(s):  
Neural Network ◽  
Linear Equations ◽  
Complex Linear

A Two-Phase Algorithm for the Chebyshev Solution of Complex Linear Equations

1994 ◽  
Vol 15 (6) ◽  
pp. 1440-1451
Author(s):  
Dirk P. Laurie ◽  
Lucas M. Venter
Keyword(s):  
Linear Equations ◽  
Two Phase ◽  
Complex Linear

Nonlinear gradient neural network for solving system of linear equations

2019 ◽  
Vol 142 ◽  
pp. 35-40 ◽  
Author(s):  
Lin Xiao ◽  
Kenli Li ◽  
Zhiguo Tan ◽  
Zhijun Zhang ◽  
Bolin Liao ◽  
...  
Keyword(s):  
Neural Network ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Gradient Neural Network

scholarly journals Identification Accuracy of Additional Wave Resistance Through a Comparison of Multiple Regression and Artificial Neural Network Methods

2018 ◽  
Vol 1 (1) ◽  
pp. 197-204
Author(s):  
Tomasz Cepowski
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Multiple Regression ◽  
Nonlinear Models ◽  
Linear Equations ◽  
Regression Method ◽  
Wave Resistance ◽  
Identification Accuracy ◽  
Linear Regression Method ◽  
Artificial Neural

Abstract The article presents the use of multiple regression method to identify added wave resistance. Added wave resistance was expressed in the form of a four-state nominal function of: “thrust”, “zero”, “minor” and “major” resistance values. Three regression models were developed for this purpose: a regression model with linear variables, nonlinear variables and a large number of nonlinear variables. The nonlinear models were developed using the author's algorithm based on heuristic techniques. The three models were compared with a model based on an artificial neural network. This study shows that non-linear equations developed through a multiple linear regression method using the author’s algorithm are relatively accurate, and in some respects, are more effective than artificial neural networks.

Towards Developing the Piece-Wise Linear Neural Network Algorithm for Rule Extraction

2020 ◽  
pp. 1632-1649
Author(s):  
Veronica Chan ◽  
Christine W. Chan
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Linear Equations ◽  
Rule Extraction ◽  
Ann Model ◽  
Factors Affecting ◽  
Artificial Neural ◽  
Linear Neural Network ◽  
Artificial Neural Network Ann ◽  
Hidden Neurons

This paper discusses development and application of a decomposition neural network rule extraction algorithm for nonlinear regression problems. The algorithm is called the piece-wise linear artificial neural network or PWL-ANN algorithm. The objective of the algorithm is to “open up” the black box of a neural network model so that rules in the form of linear equations are generated by approximating the sigmoid activation functions of the hidden neurons in an artificial neural network (ANN). The preliminary results showed that the algorithm gives high fidelity and satisfactory results on sixteen of the nineteen tested datasets. By analyzing the values of R2 given by the PWL approximation on the hidden neurons and the overall output, it is evident that in addition to accurate approximation of each individual node of a given ANN model, there are more factors affecting the fidelity of the PWL-ANN algorithm Nevertheless, the algorithm shows promising potential for domains when better understanding about the problem is needed.

A neural network training algorithm utilizing multiple sets of linear equations

1999 ◽  
Vol 25 (1-3) ◽  
pp. 55-72 ◽  
Author(s):  
Hung-Han Chen ◽  
Michael T. Manry ◽  
Hema Chandrasekaran
Keyword(s):  
Neural Network ◽  
Linear Equations ◽  
Neural Network Training ◽  
Training Algorithm ◽  
Network Training

Solving polynomial systems using a fast adaptive back propagation-type neural network algorithm

2017 ◽  
Vol 29 (2) ◽  
pp. 301-337 ◽  
Author(s):  
K. GOULIANAS ◽  
A. MARGARIS ◽  
I. REFANIDIS ◽  
K. DIAMANTARAS
Keyword(s):  
Neural Network ◽  
Adaptive Learning ◽  
Linear Equations ◽  
Back Propagation ◽  
Polynomial Systems ◽  
Optimization Techniques ◽  
Back Propagation Algorithm ◽  
Network Activation ◽  
Non Linear ◽  
Non Linear Equations

This paper proposes a neural network architecture for solving systems of non-linear equations. A back propagation algorithm is applied to solve the problem, using an adaptive learning rate procedure, based on the minimization of the mean squared error function defined by the system, as well as the network activation function, which can be linear or non-linear. The results obtained are compared with some of the standard global optimization techniques that are used for solving non-linear equations systems. The method was tested with some well-known and difficult applications (such as Gauss–Legendre 2-point formula for numerical integration, chemical equilibrium application, kinematic application, neuropsychology application, combustion application and interval arithmetic benchmark) in order to evaluate the performance of the new approach. Empirical results reveal that the proposed method is characterized by fast convergence and is able to deal with high-dimensional equations systems.

Longitudinal Control for AUV with Self-Adaptive Learning Law

2013 ◽  
Vol 819 ◽  
pp. 259-265
Author(s):  
Xiu Jun Sun ◽  
Yan Yang
Keyword(s):  
Neural Network ◽  
Adaptive Learning ◽  
Attitude Control ◽  
Autonomous Underwater Vehicle ◽  
Linear Equations ◽  
Back Propagation ◽  
Mathematic Model ◽  
Back Propagation Algorithm ◽  
Neural Network Controller ◽  
Self Adaptive

A mini AUV (Autonomous Underwater Vehicle) with cross shaped rudders and one single thruster is presented, which features high maneuverability due to the intelligent control algorithm. A single variable PID neural network controller is also proposed, which is utilized to maintain attitude for the vehicle. In order to testify feasibility of the control methodology, a spatial motion mathematic model is constructed and linear equations that indicate the relation between attitude angles of vehicle and deflection angles of rudders is deduced firstly. Subsequently, the neural network PID controller is developed according to the deduced equations and the attitude control simulation of the vehicle with this controller is conducted. Taking actual and desired attitude angles of the vehicle as input and deflection angles of the rudders as output, this controller performs self-adaptive update for 9 synaptic weights through back-propagation algorithm and employs the converged weights to calculate the appropriate deflection angle of each rudder.

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