共 46 条
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
相关论文