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

2023/08/27 by Guo, Yixiao, Ming, Pingbing · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2308.13986

Abstract

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.

Cited by

• Exact Terminal Condition Neural Network for American Option Pricing Based on the Black-Scholes-Merton Equations

Related

• Physics-Informed Neural Networks for Quantum Eigenvalue Problems
• Deep Ritz method for the spectral fractional Laplacian equation using the Caffarelli-Silvestre extension
• A new approach for the fractional Laplacian via deep neural networks
• Physics-Informed Neural Solvers for Periodic Quantum Eigenproblems
• Unsupervised Neural Networks for Quantum Eigenvalue Problems