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.

翻译：我们提出了一种计算分数阶薛定谔算子特征值的新型深度学习方法。该方法结合了新开发的损失函数与融入问题先验知识的创新神经网络架构。这些改进使我们的方法能够处理高维问题以及在不规则有界域上提出的问题。我们成功计算了多种分数阶薛定谔算子的前30个特征值。作为应用，我们分享了一个关于尚未研究的分数阶等谱问题的猜想。