Training RBF neural networks for solving nonlinear and inverse boundary value problems

被引：1

作者：

Jankowska, Malgorzata A. ^{[1
]}

Karageorghis, Andreas ^{[2
]}

Chen, C. S. ^{[3
]}

机构：

[1] Poznan Univ Tech, Inst Appl Mech, PL-60965 Poznan, Poland

[2] Univ Cyprus, Dept Math & Stat, POB 20537, CY-1678 Nicosia, Cyprus

[3] Univ Southern Mississippi, Sch Math & Nat Sci, Hattiesburg, MS 39406 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2024年 / 165卷

关键词：

RBFs; Neural networks; Kansa method; Direct BVPs; Inverse BVPs; CENTERS;

D O I：

10.1016/j.camwa.2024.04.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Radial basis function neural networks (RBFNN) have been increasingly employed to solve boundary value problems (BVPs). In the current study, we propose such a technique for nonlinear (apparently for the first time) elliptic BVPs of orders two and four in 2-D and 3-D. The method is also extended, in a natural way, to solving 2-D and 3-D inverse BVPs. The RBFNN is trained via the least squares minimization of a nonlinear functional using the MATLAB (R) routine lsqnonlin . In this way, as well as the solution, appropriate values of the RBF approximation parameters are automatically delivered. The efficacy of the proposed RBFNN is demonstrated through several numerical experiments.

引用

页码：205 / 216

页数：12

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