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 a...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.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12371438 and 12326336.
文摘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.
