JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (2): 26-36.doi: 10.6040/j.issn.1671-9352.0.2024.244

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Numerical solution of physically informed neural networks for eigenvalue problems of differential equations

TANG Yu, YUAN Lijun*   

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
  • Published:2026-02-13

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Abstract: For eigenvalue problems of differential equations, an improved physical information neural network solution and a two-stage training method are proposed. The new method can solve multiple minimum eigenvalues, the eigenvalue problem closest to the initial value and the multiple eigenvalue problem. Numerical examples of Laplace operator eigenvalue problems in 1D and 2D square regions as well as L-shaped regions show that the new method is more accurate than the existing methods.

Key words: physically informed neural networks, differential equations, eigenvalue problems

CLC Number: 

  • O242
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