首页|A Deep Learning Method for Computing Eigenvalues of the Fractional Schr?dinger Operator
A Deep Learning Method for Computing Eigenvalues of the Fractional Schr?dinger Operator
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The authors present a novel deep learning method for computing eigenvalues of the frac-tional 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.
Eigenvalue problemdeep learningfractional Schrödinger operatorisospectral problem
GUO Yixiao、MING Pingbing
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Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathe-matics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China
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