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

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

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 proces...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:International journal of mathematics and mathematical sciences 2018, Vol.2018 (2018), p.1-4
Hauptverfasser: Jaafar, Mustafa Sadeq, Zhukov, Maxim Valerievich, Gorbachenko, Vladimir Ivanovich, Alqezweeni, Mohie Mortadha
Format: Artikel
Sprache:eng
Schlagworte:
Basis functions
Boundary value problems
Computational mathematics
Computational physics
Costs
Efficiency
Meshless methods
Methods
Neural networks
Partial differential equations
Poisson equation
Radial basis function
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/2018/9457578