Unsupervised Neural Networks for Quantum Eigenvalue Problems

2020/10/10 by Henry Jin, Marios Mattheakis, Jin, Henry +3 · 7 citations
Computer Science · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Energy Load and Power Forecasting #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2010.05075

openalex publication_date 2020/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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