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A neural network training algorithm for singular perturbation boundary value problems

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Abstract

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.

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Authors and Affiliations

  1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610225, People’s Republic of China

    T. E. Simos

  2. Scientific and Educational Center “Digital Industry”, South Ural State University, 76 Lenin Ave., 454 080, Chelyabinsk, Russia

    T. E. Simos

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    T. E. Simos

  4. Data Recovery Key Laboratory of Sichun Province, Neijing Normal University, Neijiang, China

    T. E. Simos

  5. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece

    T. E. Simos

  6. microSENSES Laboratory, Department of Electrical and Electronics Engineering, University of West Attica, 250 Thivon Av., Aegaleo, 122 44, Egaleo, Greece

    Ioannis Th. Famelis

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  1. T. E. Simos
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Correspondence to T. E. Simos.

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Simos, T.E., Famelis, I.T. A neural network training algorithm for singular perturbation boundary value problems. Neural Comput & Applic 34, 607–615 (2022). https://doi.org/10.1007/s00521-021-06364-1

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