Neural Processing Letters

, Volume 50, Issue 2, pp 1153–1172 | Cite as

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

  • Hongli Sun
  • Muzhou HouEmail author
  • Yunlei Yang
  • Tianle Zhang
  • Futian Weng
  • Feng Han


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.


Bernstein neural network Extreme learning machine Differential equation 



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.

Compliance with Ethical Standards

Conflict of interest

All authors have no conflict of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaChina
  2. 2.College of ScienceHunan University of TechnologyHunanChina

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