Deep learning for inverse problems in quantum mechanics
(2021) In International Journal of Quantum Chemistry 121(9).- Abstract
Inverse problems are important in quantum mechanics and involve such questions as finding which potential give a certain spectrum or which arrangement of atoms give certain properties to a molecule or solid. Inverse problems are typically very hard to solve and tend to be very compute intense. We here show that neural networks can easily solve inverse problems in quantum mechanics. It is known that a neural network can compute the spectrum of a given potential, a result which we reproduce. We find that the (much harder) inverse problem of computing the correct potential that gives a prescribed spectrum is equally easy for a neural network. We extend previous work where neural networks were used to find the electronic many-particle... (More)
Inverse problems are important in quantum mechanics and involve such questions as finding which potential give a certain spectrum or which arrangement of atoms give certain properties to a molecule or solid. Inverse problems are typically very hard to solve and tend to be very compute intense. We here show that neural networks can easily solve inverse problems in quantum mechanics. It is known that a neural network can compute the spectrum of a given potential, a result which we reproduce. We find that the (much harder) inverse problem of computing the correct potential that gives a prescribed spectrum is equally easy for a neural network. We extend previous work where neural networks were used to find the electronic many-particle density given a potential by considering the inverse problem. That is, we show that neural networks can compute the potential that gives a prescribed many-electron density.
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- author
- Lantz, Victor ; Abiri, Najmeh LU ; Carlsson, Gillis LU and Pistol, Mats Erik LU
- organization
- publishing date
- 2021-05-05
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- deep learning, density functional theory, inverse problems, quantum mechanics
- in
- International Journal of Quantum Chemistry
- volume
- 121
- issue
- 9
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- scopus:85098444491
- ISSN
- 0020-7608
- DOI
- 10.1002/qua.26599
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2020 The Authors. International Journal of Quantum Chemistry published by Wiley Periodicals LLC. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
- id
- 4e1d90f0-d1b8-4ff9-8fbc-42fef773fd78
- date added to LUP
- 2021-03-10 13:16:17
- date last changed
- 2024-04-04 01:22:13
@article{4e1d90f0-d1b8-4ff9-8fbc-42fef773fd78,
abstract = {{<p>Inverse problems are important in quantum mechanics and involve such questions as finding which potential give a certain spectrum or which arrangement of atoms give certain properties to a molecule or solid. Inverse problems are typically very hard to solve and tend to be very compute intense. We here show that neural networks can easily solve inverse problems in quantum mechanics. It is known that a neural network can compute the spectrum of a given potential, a result which we reproduce. We find that the (much harder) inverse problem of computing the correct potential that gives a prescribed spectrum is equally easy for a neural network. We extend previous work where neural networks were used to find the electronic many-particle density given a potential by considering the inverse problem. That is, we show that neural networks can compute the potential that gives a prescribed many-electron density.</p>}},
author = {{Lantz, Victor and Abiri, Najmeh and Carlsson, Gillis and Pistol, Mats Erik}},
issn = {{0020-7608}},
keywords = {{deep learning; density functional theory; inverse problems; quantum mechanics}},
language = {{eng}},
month = {{05}},
number = {{9}},
publisher = {{John Wiley & Sons Inc.}},
series = {{International Journal of Quantum Chemistry}},
title = {{Deep learning for inverse problems in quantum mechanics}},
url = {{http://dx.doi.org/10.1002/qua.26599}},
doi = {{10.1002/qua.26599}},
volume = {{121}},
year = {{2021}},
}