Unsupervised Neural Networks for Quantum Eigenvalue Problems

Henry Jin; Marios Mattheakis; Pavlos Protopapas

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arXiv · 2010.05075

Unsupervised Neural Networks for Quantum Eigenvalue Problems

Henry Jin·Marios Mattheakis·Pavlos Protopapas

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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.

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Henry Jin, Marios Mattheakis, Pavlos Protopapas. 2020-10-10. Unsupervised Neural Networks for Quantum Eigenvalue Problems. https://arxiv.org/abs/2010.05075

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