Separable graph Hamiltonian network: A graph deep learning model for lattice systems
Addressing the challenges posed by nonlinear lattice models, which are vital across diverse scientific disciplines, we present a new deep learning approach that harnesses the power of graph neural networks. By representing the lattice system as a graph and leveraging the graph structures to identify...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
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American Physical Society
2024-02-01
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Series: | Physical Review Research |
Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013176 |
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author | Ru Geng Jian Zu Yixian Gao Hong-Kun Zhang |
author_facet | Ru Geng Jian Zu Yixian Gao Hong-Kun Zhang |
author_sort | Ru Geng |
collection | DOAJ |
description | Addressing the challenges posed by nonlinear lattice models, which are vital across diverse scientific disciplines, we present a new deep learning approach that harnesses the power of graph neural networks. By representing the lattice system as a graph and leveraging the graph structures to identify complex nonlinear relationships, we have developed a flexible solution that outperforms traditional techniques. Our model not only offers precise trajectory predictions and energy conservation properties by incorporating separable Hamiltonians but also proves superior to existing top-tier models when tested on classic nonlinear oscillator lattice problems: a mixed Fermi-Pasta-Ulam Klein-Gordon, a Klein-Gordon system with long-range interactions, and a two-dimensional Frenkel-Kontorova, highlighting its potential for wide-reaching applications. |
first_indexed | 2024-04-24T10:07:16Z |
format | Article |
id | doaj.art-501c02c069344432b08e3e3c71e3b7ef |
institution | Directory Open Access Journal |
issn | 2643-1564 |
language | English |
last_indexed | 2024-04-24T10:07:16Z |
publishDate | 2024-02-01 |
publisher | American Physical Society |
record_format | Article |
series | Physical Review Research |
spelling | doaj.art-501c02c069344432b08e3e3c71e3b7ef2024-04-12T17:39:16ZengAmerican Physical SocietyPhysical Review Research2643-15642024-02-016101317610.1103/PhysRevResearch.6.013176Separable graph Hamiltonian network: A graph deep learning model for lattice systemsRu GengJian ZuYixian GaoHong-Kun ZhangAddressing the challenges posed by nonlinear lattice models, which are vital across diverse scientific disciplines, we present a new deep learning approach that harnesses the power of graph neural networks. By representing the lattice system as a graph and leveraging the graph structures to identify complex nonlinear relationships, we have developed a flexible solution that outperforms traditional techniques. Our model not only offers precise trajectory predictions and energy conservation properties by incorporating separable Hamiltonians but also proves superior to existing top-tier models when tested on classic nonlinear oscillator lattice problems: a mixed Fermi-Pasta-Ulam Klein-Gordon, a Klein-Gordon system with long-range interactions, and a two-dimensional Frenkel-Kontorova, highlighting its potential for wide-reaching applications.http://doi.org/10.1103/PhysRevResearch.6.013176 |
spellingShingle | Ru Geng Jian Zu Yixian Gao Hong-Kun Zhang Separable graph Hamiltonian network: A graph deep learning model for lattice systems Physical Review Research |
title | Separable graph Hamiltonian network: A graph deep learning model for lattice systems |
title_full | Separable graph Hamiltonian network: A graph deep learning model for lattice systems |
title_fullStr | Separable graph Hamiltonian network: A graph deep learning model for lattice systems |
title_full_unstemmed | Separable graph Hamiltonian network: A graph deep learning model for lattice systems |
title_short | Separable graph Hamiltonian network: A graph deep learning model for lattice systems |
title_sort | separable graph hamiltonian network a graph deep learning model for lattice systems |
url | http://doi.org/10.1103/PhysRevResearch.6.013176 |
work_keys_str_mv | AT rugeng separablegraphhamiltoniannetworkagraphdeeplearningmodelforlatticesystems AT jianzu separablegraphhamiltoniannetworkagraphdeeplearningmodelforlatticesystems AT yixiangao separablegraphhamiltoniannetworkagraphdeeplearningmodelforlatticesystems AT hongkunzhang separablegraphhamiltoniannetworkagraphdeeplearningmodelforlatticesystems |