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The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method
How to solve the numerical solution of nonlinear partial differential equations efficiently and conveniently has always been a difficult and meaningful problem. In this paper, the data-driven quasiperiodic wave, periodic wave, and soliton solutions of the KdV-mKdV equation are simulated by the multi...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Hindawi
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8642030/ https://www.ncbi.nlm.nih.gov/pubmed/34868298 http://dx.doi.org/10.1155/2021/8548482 |
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author | Zhang, Yong Dong, Huanhe Sun, Jiuyun Wang, Zhen Fang, Yong Kong, Yuan |
author_facet | Zhang, Yong Dong, Huanhe Sun, Jiuyun Wang, Zhen Fang, Yong Kong, Yuan |
author_sort | Zhang, Yong |
collection | PubMed |
description | How to solve the numerical solution of nonlinear partial differential equations efficiently and conveniently has always been a difficult and meaningful problem. In this paper, the data-driven quasiperiodic wave, periodic wave, and soliton solutions of the KdV-mKdV equation are simulated by the multilayer physics-informed neural networks (PINNs) and compared with the exact solution obtained by the generalized Jacobi elliptic function method. Firstly, the different types of solitary wave solutions are used as initial data to train the PINNs. At the same time, the different PINNs are applied to learn the same initial data by selecting the different numbers of initial points sampled, residual collocation points sampled, network layers, and neurons per hidden layer, respectively. The result shows that the PINNs well reconstruct the dynamical behaviors of the quasiperiodic wave, periodic wave, and soliton solutions for the KdV-mKdV equation, which gives a good way to simulate the solutions of nonlinear partial differential equations via one deep learning method. |
format | Online Article Text |
id | pubmed-8642030 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Hindawi |
record_format | MEDLINE/PubMed |
spelling | pubmed-86420302021-12-04 The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method Zhang, Yong Dong, Huanhe Sun, Jiuyun Wang, Zhen Fang, Yong Kong, Yuan Comput Intell Neurosci Research Article How to solve the numerical solution of nonlinear partial differential equations efficiently and conveniently has always been a difficult and meaningful problem. In this paper, the data-driven quasiperiodic wave, periodic wave, and soliton solutions of the KdV-mKdV equation are simulated by the multilayer physics-informed neural networks (PINNs) and compared with the exact solution obtained by the generalized Jacobi elliptic function method. Firstly, the different types of solitary wave solutions are used as initial data to train the PINNs. At the same time, the different PINNs are applied to learn the same initial data by selecting the different numbers of initial points sampled, residual collocation points sampled, network layers, and neurons per hidden layer, respectively. The result shows that the PINNs well reconstruct the dynamical behaviors of the quasiperiodic wave, periodic wave, and soliton solutions for the KdV-mKdV equation, which gives a good way to simulate the solutions of nonlinear partial differential equations via one deep learning method. Hindawi 2021-11-26 /pmc/articles/PMC8642030/ /pubmed/34868298 http://dx.doi.org/10.1155/2021/8548482 Text en Copyright © 2021 Yong Zhang et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Research Article Zhang, Yong Dong, Huanhe Sun, Jiuyun Wang, Zhen Fang, Yong Kong, Yuan The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method |
title | The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method |
title_full | The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method |
title_fullStr | The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method |
title_full_unstemmed | The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method |
title_short | The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method |
title_sort | new simulation of quasiperiodic wave, periodic wave, and soliton solutions of the kdv-mkdv equation via a deep learning method |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8642030/ https://www.ncbi.nlm.nih.gov/pubmed/34868298 http://dx.doi.org/10.1155/2021/8548482 |
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