A neural network training algorithm for singular perturbation boundary value problems

被引：6

作者：

Simos, T. E. ^{[1
,2
,3
,4
,5
]}

Famelis, Ioannis Th ^{[6
]}

机构：

[1] Chengdu Univ Informat Technol, Coll Appl Math, Chengdu 610225, Peoples R China

[2] South Ural State Univ, Sci & Educ Ctr Digital Ind, 76 Lenin Ave, Chelyabinsk 454080, Russia

[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[4] Neijing Normal Univ, Data Recovery Key Lab Sichun Prov, Neijiang, Peoples R China

[5] Democritus Univ Thrace, Dept Civil Engn, Sect Math, Xanthi, Greece

[6] Univ West Attica, Dept Elect & Elect Engn, MicroSENSES Lab, 250 Thivon Av, Aegaleo 12244, Egaleo, Greece

来源：

NEURAL COMPUTING & APPLICATIONS | 2022年 / 34卷 / 01期

关键词：

Computational intelligence; Neural Networks; Singular Perturbation Boundary Value Problems; NUMERICAL-SOLUTION; SOLVING ORDINARY; SYSTEMS; SPLINE;

D O I：

10.1007/s00521-021-06364-1

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A training algorithm for the Neural Network solution of Singular Perturbation Boundary Value Problems is presented. The solution is based on a single hidden layer feed forward Neural Network with a small number of neurons. The training algorithm adapts the training points grid so to be more tense in areas of the integration interval that solution has a layer or a peek. The algorithm automatically detects the areas of interest in the integration interval. The resulted Neural Network solutions are very accurate in a uniform way. The numerical tests in various test problems justify our arguments as the produced solutions prove to give smaller errors compare to their competitors.

引用

页码：607 / 615

页数：9

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