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

被引:1
作者
Guo Yixiao [1 ,2 ]
Ming Pingbing [1 ,2 ]
机构
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
基金
中国国家自然科学基金;
关键词
Eigenvalue problem; deep learning; fractional Schrodinger operator; isospectral problem; NUMERICAL-METHODS; NEURAL-NETWORKS; SPECTRAL METHOD; LAPLACIAN; DOMAINS; DIFFUSION; EFFICIENT; DYNAMICS; SPHERES; SHAPE;
D O I
10.1007/s11424-024-3250-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The authors present a novel deep learning method for computing eigenvalues of the fractional Schrodinger 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 Schrodinger operators. As an application, the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.
引用
收藏
页码:391 / 412
页数:22
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