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Genetic Programming Symbolic Regression with Simplification-Pruning Operator for Solving Differential Equations

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Neural Information Processing (ICONIP 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1962))

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Abstract

Differential equations (DEs) are important mathematical models for describing natural phenomena and engineering problems. Finding analytical solutions for DEs has theoretical and practical benefits. However, traditional methods for finding analytical solutions only work for some special forms of DEs, such as separable variables or transformable to ordinary differential equations. For general nonlinear DEs, analytical solutions are often hard to obtain. The current popular method based on neural networks requires a lot of data to train the network and only gives approximate solutions with errors and instability. It is also a black-box model that is not interpretable. To obtain analytical solutions for DEs, this paper proposes a symbolic regression algorithm based on genetic programming with the simplification-pruning operator (SP-GPSR). This method introduces a new operator that can simplify the individual expressions in the population and randomly remove some structures in the formulas. Moreover, this method uses multiple fitness functions that consider the accuracy of the analytic solution satisfying the sampled data and the differential equations. In addition, this algorithm also uses a hybrid optimization technique to improve search efficiency and convergence speed. This paper conducts experiments on two typical classes of DEs. The results show that the proposed method can effectively find analytical solutions for DEs with high accuracy and simplicity.

This work was partly supported by the National Natural Science Foundation of China under Grant No. 62276222.

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Authors and Affiliations

  1. School of Informatics, Xiamen University, Fujian, China

    Lulu Cao, Zimo Zheng & Min Jiang

  2. College of Engineering, Shantou University, Guangdong, China

    Chenwen Ding

  3. School of Information Science and Technology, Hainan Normal University, Hainan, China

    Jinkai Cai

Authors
  1. Lulu Cao
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  2. Zimo Zheng
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  3. Chenwen Ding
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  4. Jinkai Cai
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  5. Min Jiang
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Corresponding author

Correspondence to Min Jiang .

Editor information

Editors and Affiliations

  1. School of Automation, Central South University, Changsha, China

    Biao Luo

  2. Institute of Automation, Chinese Academy of Sciences, Beijing, China

    Long Cheng

  3. Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China

    Zheng-Guang Wu

  4. School of Automation, Guangdong University of Technology, Guangzhou, China

    Hongyi Li

  5. School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW, Australia

    Chaojie Li

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© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Cao, L., Zheng, Z., Ding, C., Cai, J., Jiang, M. (2024). Genetic Programming Symbolic Regression with Simplification-Pruning Operator for Solving Differential Equations. In: Luo, B., Cheng, L., Wu, ZG., Li, H., Li, C. (eds) Neural Information Processing. ICONIP 2023. Communications in Computer and Information Science, vol 1962. Springer, Singapore. https://doi.org/10.1007/978-981-99-8132-8_22

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  • DOI: https://doi.org/10.1007/978-981-99-8132-8_22

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-8131-1

  • Online ISBN: 978-981-99-8132-8

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