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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/9457578 |
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| _version_ | 1849412301320355840 |
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| author | Mohie Mortadha Alqezweeni Vladimir Ivanovich Gorbachenko Maxim Valerievich Zhukov Mustafa Sadeq Jaafar |
| author_facet | Mohie Mortadha Alqezweeni Vladimir Ivanovich Gorbachenko Maxim Valerievich Zhukov Mustafa Sadeq Jaafar |
| author_sort | Mohie Mortadha Alqezweeni |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-63fcadd5b01d46008f26bf7db7904866 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-63fcadd5b01d46008f26bf7db79048662025-08-20T03:34:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/94575789457578Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region MethodMohie Mortadha Alqezweeni0Vladimir Ivanovich Gorbachenko1Maxim Valerievich Zhukov2Mustafa Sadeq Jaafar3Penza State University, Penza, RussiaPenza State University, Penza, RussiaPenza State University, Penza, RussiaPenza State University, Penza, RussiaA 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.http://dx.doi.org/10.1155/2018/9457578 |
| spellingShingle | Mohie Mortadha Alqezweeni Vladimir Ivanovich Gorbachenko Maxim Valerievich Zhukov Mustafa Sadeq Jaafar Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method International Journal of Mathematics and Mathematical Sciences |
| title | Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method |
| title_full | Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method |
| title_fullStr | Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method |
| title_full_unstemmed | Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method |
| title_short | Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method |
| title_sort | efficient solving of boundary value problems using radial basis function networks learned by trust region method |
| url | http://dx.doi.org/10.1155/2018/9457578 |
| work_keys_str_mv | AT mohiemortadhaalqezweeni efficientsolvingofboundaryvalueproblemsusingradialbasisfunctionnetworkslearnedbytrustregionmethod AT vladimirivanovichgorbachenko efficientsolvingofboundaryvalueproblemsusingradialbasisfunctionnetworkslearnedbytrustregionmethod AT maximvalerievichzhukov efficientsolvingofboundaryvalueproblemsusingradialbasisfunctionnetworkslearnedbytrustregionmethod AT mustafasadeqjaafar efficientsolvingofboundaryvalueproblemsusingradialbasisfunctionnetworkslearnedbytrustregionmethod |