Unsupervised Neural Networks for Quantum Eigenvalue Problems
Computational Physics
2020-10-13 v1 Machine Learning
Abstract
Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that identically satisfy the boundary conditions. A scanning mechanism is embedded allowing the method to find an arbitrary number of solutions. The network optimization is data-free and depends solely on the predictions. The unsupervised method is used to solve the quantum infinite well and quantum oscillator eigenvalue problems.
Cite
@article{arxiv.2010.05075,
title = {Unsupervised Neural Networks for Quantum Eigenvalue Problems},
author = {Henry Jin and Marios Mattheakis and Pavlos Protopapas},
journal= {arXiv preprint arXiv:2010.05075},
year = {2020}
}
Comments
5 pages, 3 figures