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Learning solution of a bond-based linear peridynamic model using LS-SVR method

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  • Ma, Jie
  • Yang, Zhiwei
  • Du, Ning

Abstract

In this paper, we develop an efficient least squares support vector regression (LS-SVR) method for a steady-state bond-based linear Peridynamic (PD) model in two space dimensions. To minimize a residual function associated with PD model, we introduce some dual variables to rewrite the optimization problem to a linear system and obtain a closed form approximate solution of the considered problem. The method is suitable to solve PD problem involving singular kernel, irregular geometrical domains. Numerical experiments are provided to show the accuracy and efficiency of the proposed method.

Suggested Citation

  • Ma, Jie & Yang, Zhiwei & Du, Ning, 2024. "Learning solution of a bond-based linear peridynamic model using LS-SVR method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 262-272.
    • Handle: RePEc:eee:matcom:v:217:y:2024:i:c:p:262-272
    DOI: 10.1016/j.matcom.2023.10.016
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    References listed on IDEAS

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    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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