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arXiv · 2308.13986

A Deep Learning Method for Computing Eigenvalues of the Fractional Schr\"odinger Operator

Yixiao Guo·Pingbing Ming
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Abstract

We present a novel deep learning method for computing eigenvalues of the fractional Schr\"odinger 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 Schr\"odinger operators. As an application, we share a conjecture to the fractional order isospectral problem that has not yet been studied.

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Yixiao Guo, Pingbing Ming. 2023-08-27. A Deep Learning Method for Computing Eigenvalues of the Fractional Schr\"odinger Operator. https://arxiv.org/abs/2308.13986

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