Unsupervised Neural Networks for Quantum Eigenvalue Problems

• URL: http://arxiv.org/abs/2010.05075v1
• Date: Sat, 10 Oct 2020 19:34:37 GMT
• Title: Unsupervised Neural Networks for Quantum Eigenvalue Problems
• Authors: Henry Jin, Marios Mattheakis, Pavlos Protopapas
• Abstract summary: We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. A scanning mechanism is embedded allowing the method to find an arbitrary number of solutions.
• Score: 1.2891210250935146
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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