Solving boundary value problems of mathematical physics using radial basis function networks

2017 ◽  
Vol 57 (1) ◽  
pp. 145-155 ◽  
Author(s):  
V. I. Gorbachenko ◽  
M. V. Zhukov
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Mathematical Physics ◽  
Radial Basis Function Networks ◽  
Radial Basis

scholarly journals Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Mohie Mortadha Alqezweeni ◽  
Vladimir Ivanovich Gorbachenko ◽  
Maxim Valerievich Zhukov ◽  
Mustafa Sadeq Jaafar
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Trust Region Method ◽  
Trust Region ◽  
Radial Basis Function Networks ◽  
Structure Selection ◽  
Region Method ◽  
Radial Basis

A method using radial basis function networks (RBFNs) to solve boundary value problems of mathematical physics is presented in this paper. The main advantages of mesh-free methods based on RBFN are explained here. To learn RBFNs, the Trust Region Method (TRM) is proposed, which simplifies the process of network structure selection and reduces time expenses to adjust their parameters. Application of the proposed algorithm is illustrated by solving two-dimensional Poisson equation.

scholarly journals The Conical Radial Basis Function for Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
J. Zhang ◽  
F. Z. Wang ◽  
E. R. Hou
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Computational Cost ◽  
Basis Functions ◽  
Simple Scheme ◽  
Collocation Points ◽  
Radial Basis ◽  
Radial Basis Function Method

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.

Universal Approximation Using Radial-Basis-Function Networks

1991 ◽  
Vol 3 (2) ◽  
pp. 246-257 ◽  
Author(s):  
J. Park ◽  
I. W. Sandberg
Keyword(s):  
Finite Number ◽  
Radial Basis Function ◽  
Basis Function ◽  
Universal Approximation ◽  
Radial Basis Function Networks ◽  
Feedforward Networks ◽  
Rbf Networks ◽  
Smoothing Factor ◽  
Radial Basis ◽  
Hidden Layer

There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units. This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.

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