Visualizing a neural network that develops quantum perturbation theory
Motivated by the question whether the empirical fitting of data by neural networks can yield the same structure of physical laws, we apply neural networks to a quantum-mechanical two-body scattering problem with short-range potentials—a problem that by itself plays an important role in many branches...
Main Authors: | , , , |
---|---|
Other Authors: | |
Format: | Article |
Language: | English |
Published: |
American Physical Society
2018
|
Online Access: | http://hdl.handle.net/1721.1/117207 https://orcid.org/0000-0003-1667-8011 |
_version_ | 1811078486889070592 |
---|---|
author | Wu, Yadong Zhang, Pengfei Shen, Huitao Zhai, Hui |
author2 | Massachusetts Institute of Technology. Department of Physics |
author_facet | Massachusetts Institute of Technology. Department of Physics Wu, Yadong Zhang, Pengfei Shen, Huitao Zhai, Hui |
author_sort | Wu, Yadong |
collection | MIT |
description | Motivated by the question whether the empirical fitting of data by neural networks can yield the same structure of physical laws, we apply neural networks to a quantum-mechanical two-body scattering problem with short-range potentials—a problem that by itself plays an important role in many branches of physics. After training, the neural network can accurately predict s-wave scattering length, which governs the low-energy scattering physics. By visualizing the neural network, we show that it develops perturbation theory order by order when the potential depth increases, without solving the Schrödinger equation or obtaining the wave function explicitly. The result provides an important benchmark to the machine-assisted physics research or even automated machine learning physics laws. |
first_indexed | 2024-09-23T11:00:44Z |
format | Article |
id | mit-1721.1/117207 |
institution | Massachusetts Institute of Technology |
language | English |
last_indexed | 2024-09-23T11:00:44Z |
publishDate | 2018 |
publisher | American Physical Society |
record_format | dspace |
spelling | mit-1721.1/1172072022-10-01T00:34:22Z Visualizing a neural network that develops quantum perturbation theory Wu, Yadong Zhang, Pengfei Shen, Huitao Zhai, Hui Massachusetts Institute of Technology. Department of Physics Shen, Huitao Motivated by the question whether the empirical fitting of data by neural networks can yield the same structure of physical laws, we apply neural networks to a quantum-mechanical two-body scattering problem with short-range potentials—a problem that by itself plays an important role in many branches of physics. After training, the neural network can accurately predict s-wave scattering length, which governs the low-energy scattering physics. By visualizing the neural network, we show that it develops perturbation theory order by order when the potential depth increases, without solving the Schrödinger equation or obtaining the wave function explicitly. The result provides an important benchmark to the machine-assisted physics research or even automated machine learning physics laws. 2018-07-31T12:05:34Z 2018-07-31T12:05:34Z 2018-07 2018-03 2018-07-30T16:18:11Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 http://hdl.handle.net/1721.1/117207 Wu, Yadong, Pengfei Zhang, Huitao Shen and Hui Zhai. "Visualizing a neural network that develops quantum perturbation theory." Physucial Review A 98 (2018), 010701. https://orcid.org/0000-0003-1667-8011 en http://dx.doi.org/10.1103/PhysRevA.98.010701 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
spellingShingle | Wu, Yadong Zhang, Pengfei Shen, Huitao Zhai, Hui Visualizing a neural network that develops quantum perturbation theory |
title | Visualizing a neural network that develops quantum perturbation theory |
title_full | Visualizing a neural network that develops quantum perturbation theory |
title_fullStr | Visualizing a neural network that develops quantum perturbation theory |
title_full_unstemmed | Visualizing a neural network that develops quantum perturbation theory |
title_short | Visualizing a neural network that develops quantum perturbation theory |
title_sort | visualizing a neural network that develops quantum perturbation theory |
url | http://hdl.handle.net/1721.1/117207 https://orcid.org/0000-0003-1667-8011 |
work_keys_str_mv | AT wuyadong visualizinganeuralnetworkthatdevelopsquantumperturbationtheory AT zhangpengfei visualizinganeuralnetworkthatdevelopsquantumperturbationtheory AT shenhuitao visualizinganeuralnetworkthatdevelopsquantumperturbationtheory AT zhaihui visualizinganeuralnetworkthatdevelopsquantumperturbationtheory |