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Parameter Identification Inverse Problems of Partial Differential Equations Based on the Improved Gene Expression Programming

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High Performance Computing and Applications (HPCA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9576))

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Abstract

Traditionally, solving the parameter identification inverse problems of partial differential equations encountered many difficulties and insufficiency. In this paper, we propose an improved GEP (Gene Expression Programming) to identify the parameters in the reverse problems of partial differential equations based on the self-adaption, self-organization and self-learning characters of GEP. This algorithm simulates a parametric function itself of a partial differential equation directly through the observed values by fully taking into account inverse results caused by noises of a measured value. Modeling is unnecessary to add regularization in the modeling process aiming at special problems again. The experiment results show that the algorithm has good noise-immunity. In case there is no noise or noise is very low, the identified parametric function is almost the same as the original accurate value; when noise is very high, good results can still be obtained, which successfully realizes automation of the parameter modeling process for partial differential equations.

This work was supported by the Technology Planning Project of Guangdong Province of China with the Grant No. 2015A020209108

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Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Yan Chen & Kangshun Li

  2. Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

    Yan Chen & Zhangxin Chen

Authors
  1. Yan Chen
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  2. Kangshun Li
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  3. Zhangxin Chen
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Corresponding author

Correspondence to Zhangxin Chen .

Editor information

Editors and Affiliations

  1. School of Computer Engineering, Shanghai University, Shanghai, China

    Jiang Xie

  2. Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada

    Zhangxin Chen

  3. Mathematics Department, University of Wyoming, Laramie, Wyoming, USA

    Craig C. Douglas

  4. School of Computer Engineering, Shanghai University, Shanghai, China

    Wu Zhang

  5. Mathematics and Informatics, South China Agricultural University, Guangzhou, China

    Yan Chen

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Chen, Y., Li, K., Chen, Z. (2016). Parameter Identification Inverse Problems of Partial Differential Equations Based on the Improved Gene Expression Programming. In: Xie, J., Chen, Z., Douglas, C., Zhang, W., Chen, Y. (eds) High Performance Computing and Applications. HPCA 2015. Lecture Notes in Computer Science(), vol 9576. Springer, Cham. https://doi.org/10.1007/978-3-319-32557-6_24

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  • DOI: https://doi.org/10.1007/978-3-319-32557-6_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32556-9

  • Online ISBN: 978-3-319-32557-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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