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Solving Partial Differential Equation Based on Bernstein Neural Network and Extreme Learning Machine Algorithm

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Abstract

In this paper, we introduce a new method based on Bernstein Neural Network model (BeNN) and extreme learning machine algorithm to solve the differential equation. In the proposed method, we develop a single-layer functional link BeNN, the hidden layer is eliminated by expanding the input pattern by Bernstein polynomials. The network parameters are obtained by solving a system of linear equations using the extreme learning machine algorithm. Finally, the numerical experiment is carried out by MATLAB, results obtained are compared with the existing method, which proves the feasibility and superiority of the proposed method.

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Acknowledgements

This study was funded by the National Natural Science Foundation of China under Grants 61375063, 61271355, 11301549 and 11271378. This study was also funded by the Central South University Caitian Xuanzhu student innovation and business Projects 201710533542.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Hongli Sun, Muzhou Hou, Yunlei Yang, Tianle Zhang & Futian Weng

  2. College of Science, Hunan University of Technology, Hunan, China

    Feng Han

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  1. Hongli Sun
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  2. Muzhou Hou
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  3. Yunlei Yang
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  4. Tianle Zhang
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  5. Futian Weng
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  6. Feng Han
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Correspondence to Muzhou Hou.

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Sun, H., Hou, M., Yang, Y. et al. Solving Partial Differential Equation Based on Bernstein Neural Network and Extreme Learning Machine Algorithm. Neural Process Lett 50, 1153–1172 (2019). https://doi.org/10.1007/s11063-018-9911-8

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