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

08/27/2023

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by   Yixiao Guo, et al.

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