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A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator

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Abstract

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator. The proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the problem. These improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded domains. The authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger operators. As an application, the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

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Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yixiao Guo & Pingbing Ming

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yixiao Guo & Pingbing Ming

Authors
  1. Yixiao Guo
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  2. Pingbing Ming
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Corresponding author

Correspondence to Pingbing Ming.

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The authors declare no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 12371438 and 12326336.

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Guo, Y., Ming, P. A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator. J Syst Sci Complex 37, 391–412 (2024). https://doi.org/10.1007/s11424-024-3250-9

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  • DOI: https://doi.org/10.1007/s11424-024-3250-9

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