Numerical solution of PDEs via integrated radial basis function networks with adaptive training algorithm

2011 ◽  
Vol 11 (1) ◽  
pp. 855-860 ◽  
Author(s):  
Hong Chen ◽  
Li Kong ◽  
Wen-Jun Leng
Keyword(s):  
Radial Basis Function ◽  
Numerical Solution ◽  
Basis Function ◽  
Radial Basis Function Networks ◽  
Training Algorithm ◽  
Adaptive Training ◽  
Radial Basis

scholarly journals Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Mohammad Mehdi Mazarei ◽  
Azim Aminataei
Keyword(s):  
Radial Basis Function ◽  
Numerical Solution ◽  
Condition Number ◽  
Basis Function ◽  
Elliptic Partial Differential Equations ◽  
Basis Functions ◽  
Poisson’S Equation ◽  
Radial Basis Function Networks ◽  
Poisson's Equation ◽  
Radial Basis

This paper presents numerical solution of elliptic partial differential equations (Poisson's equation) using a combination of logarithmic and multiquadric radial basis function networks. This method uses a special combination between logarithmic and multiquadric radial basis functions with a parameterr. Further, the condition number which arises in the process is discussed, and a comparison is made between them with our earlier studies and previously known ones. It is shown that the system is stable.

scholarly journals An Improved Radial Basis Function Networks in Networks Weights Adjustment for Training Real-World Nonlinear Datasets

2019 ◽  
Vol 8 (1) ◽  
pp. 63
Author(s):  
Lim Eng Aik ◽  
Tan Wei Hong ◽  
Ahmad Kadri Junoh
Keyword(s):  
Neural Networks ◽  
Radial Basis Function ◽  
Real World ◽  
Basis Function ◽  
Gradient Descent ◽  
Radial Basis Function Networks ◽  
Training Algorithm ◽  
Descent Algorithm ◽  
Gradient Descent Algorithm ◽  
Radial Basis

In neural networks, the accuracies of its networks are mainly relying on two important factors which are the centers and the networks weight. The gradient descent algorithm is a widely used weight adjustment algorithm in most of neural networks training algorithm. However, the method is known for its weakness for easily trap in local minima. It suffers from a random weight generated for the networks during initial stage of training at input layer to hidden layer networks. The performance of radial basis function networks (RBFN) has been improved from different perspectives, including centroid initialization problem to weight correction stage over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the weight produces by the algorithm. To solve this problem, an improved gradient descent algorithm for finding initial weight and improve the overall networks weight is proposed. This improved version algorithm is incorporated into RBFN training algorithm for updating weight. Hence, this paper presented an improved RBFN in term of algorithm for improving the weight adjustment in RBFN during training process. The proposed training algorithm, which uses improved gradient descent algorithm for weight adjustment for training RBFN, obtained significant improvement in predictions compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment. The proposed improved network called IRBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to IRBFN for root mean square error (RMSE) values with standard RBFN. The IRBFN yielded a promising result with an average improvement percentage more than 40 percent in RMSE.

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