Numerical Solutions of Differential Equations using Artificial Neural Networks

Detalhes bibliográficos
Autor(a) principal: Aroztegui, José Miguel
Data de Publicação: 2021
Outros Autores: Machado, Thiago José
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Vetor (Online)
Texto Completo: https://periodicos.furg.br/vetor/article/view/13793
Resumo: In this article, we study a way to numerically solve differential equations using neural networks. Basically, we rewrite the differential equation as an optimization problem, where the parameters related  to the neural network are optimized. The proposal of this work constitutes a variation of the formulation introduced by Lagaris et al. [1], differing mainly in the form of the construction of the approximate solution. Although we only deal with first and second order ordinary differential equations, the numerical results show the efficiency of the proposed method. Furthermore, this method has a great potential, due to the amount of differential operators and applications in which it can be used.
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spelling Numerical Solutions of Differential Equations using Artificial Neural NetworksSoluções Numéricas de Equações Diferenciais com Redes Neurais ArtificiaisNeural networksDifferential equationsOptimizationRedes neuraisEquações diferenciaisOtimizaçãoIn this article, we study a way to numerically solve differential equations using neural networks. Basically, we rewrite the differential equation as an optimization problem, where the parameters related  to the neural network are optimized. The proposal of this work constitutes a variation of the formulation introduced by Lagaris et al. [1], differing mainly in the form of the construction of the approximate solution. Although we only deal with first and second order ordinary differential equations, the numerical results show the efficiency of the proposed method. Furthermore, this method has a great potential, due to the amount of differential operators and applications in which it can be used.Neste artigo, vamos estudar uma forma de resolver numericamente equações diferenciais utilizando redes neurais. Basicamente, reescrevemos a equação diferencial como um problema de otimização, onde os parâmetros associados à rede neural são otimizados. A proposta deste trabalho apresentada aqui constitui uma variação da formulação introduzida por Lagaris et al. [1], diferenciando-se principalmente na forma de construção da solução aproximada. Apesar de lidarmos apenas com equações diferenciais ordinárias de primeira e segunda ordens, os resultados numéricos mostram a eficiência do método proposto. Além disso, ele possui bastante potencial, devido a quantidade de equações diferenciais e aplicações nas quais ele pode ser utilizado.Universidade Federal do Rio Grande2021-12-17info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.furg.br/vetor/article/view/1379310.14295/vetor.v31i2.13793VETOR - Journal of Exact Sciences and Engineering; Vol. 31 No. 2 (2021); 2-13VETOR - Revista de Ciências Exatas e Engenharias; v. 31 n. 2 (2021); 2-132358-34520102-7352reponame:Vetor (Online)instname:Universidade Federal do Rio Grande (FURG)instacron:FURGenghttps://periodicos.furg.br/vetor/article/view/13793/9138Copyright (c) 2021 VETOR - Revista de Ciências Exatas e Engenhariasinfo:eu-repo/semantics/openAccessAroztegui, José MiguelMachado, Thiago José2021-12-17T12:22:06Zoai:periodicos.furg.br:article/13793Revistahttps://periodicos.furg.br/vetorPUBhttps://periodicos.furg.br/vetor/oaigmplatt@furg.br2358-34520102-7352opendoar:2021-12-17T12:22:06Vetor (Online) - Universidade Federal do Rio Grande (FURG)false
dc.title.none.fl_str_mv Numerical Solutions of Differential Equations using Artificial Neural Networks
Soluções Numéricas de Equações Diferenciais com Redes Neurais Artificiais
title Numerical Solutions of Differential Equations using Artificial Neural Networks
spellingShingle Numerical Solutions of Differential Equations using Artificial Neural Networks
Aroztegui, José Miguel
Neural networks
Differential equations
Optimization
Redes neurais
Equações diferenciais
Otimização
title_short Numerical Solutions of Differential Equations using Artificial Neural Networks
title_full Numerical Solutions of Differential Equations using Artificial Neural Networks
title_fullStr Numerical Solutions of Differential Equations using Artificial Neural Networks
title_full_unstemmed Numerical Solutions of Differential Equations using Artificial Neural Networks
title_sort Numerical Solutions of Differential Equations using Artificial Neural Networks
author Aroztegui, José Miguel
author_facet Aroztegui, José Miguel
Machado, Thiago José
author_role author
author2 Machado, Thiago José
author2_role author
dc.contributor.author.fl_str_mv Aroztegui, José Miguel
Machado, Thiago José
dc.subject.por.fl_str_mv Neural networks
Differential equations
Optimization
Redes neurais
Equações diferenciais
Otimização
topic Neural networks
Differential equations
Optimization
Redes neurais
Equações diferenciais
Otimização
description In this article, we study a way to numerically solve differential equations using neural networks. Basically, we rewrite the differential equation as an optimization problem, where the parameters related  to the neural network are optimized. The proposal of this work constitutes a variation of the formulation introduced by Lagaris et al. [1], differing mainly in the form of the construction of the approximate solution. Although we only deal with first and second order ordinary differential equations, the numerical results show the efficiency of the proposed method. Furthermore, this method has a great potential, due to the amount of differential operators and applications in which it can be used.
publishDate 2021
dc.date.none.fl_str_mv 2021-12-17
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.furg.br/vetor/article/view/13793
10.14295/vetor.v31i2.13793
url https://periodicos.furg.br/vetor/article/view/13793
identifier_str_mv 10.14295/vetor.v31i2.13793
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://periodicos.furg.br/vetor/article/view/13793/9138
dc.rights.driver.fl_str_mv Copyright (c) 2021 VETOR - Revista de Ciências Exatas e Engenharias
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2021 VETOR - Revista de Ciências Exatas e Engenharias
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal do Rio Grande
publisher.none.fl_str_mv Universidade Federal do Rio Grande
dc.source.none.fl_str_mv VETOR - Journal of Exact Sciences and Engineering; Vol. 31 No. 2 (2021); 2-13
VETOR - Revista de Ciências Exatas e Engenharias; v. 31 n. 2 (2021); 2-13
2358-3452
0102-7352
reponame:Vetor (Online)
instname:Universidade Federal do Rio Grande (FURG)
instacron:FURG
instname_str Universidade Federal do Rio Grande (FURG)
instacron_str FURG
institution FURG
reponame_str Vetor (Online)
collection Vetor (Online)
repository.name.fl_str_mv Vetor (Online) - Universidade Federal do Rio Grande (FURG)
repository.mail.fl_str_mv gmplatt@furg.br
_version_ 1797041760344473600

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