ANN与相对论等温气体球的解析解

IF 1.1 4区物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS

Revista Mexicana de Astronomia y Astrofisica Pub Date : 2022-10-01 DOI:10.22201/ia.01851101p.2022.58.02.13

M. Nouh, Y. A. Azzam, E. Abdel-salam, F. Elnagahy, T. M. Kamel

{"title":"ANN与相对论等温气体球的解析解","authors":"M. Nouh, Y. A. Azzam, E. Abdel-salam, F. Elnagahy, T. M. Kamel","doi":"10.22201/ia.01851101p.2022.58.02.13","DOIUrl":null,"url":null,"abstract":"Relativistic isothermal gas spheres are a powerful tool to model many astronomical objects, like compact stars and clusters of galaxies. In the present paper, we introduce an artificial neural network (ANN) algorithm and Taylor series to model the relativistic gas spheres using Tolman-Oppenheimer-Volkoff differential equations (TOV). Comparing the analytical solutions with the numerical ones revealed good agreement with maximum relative errors of 10−3. The ANN algorithm implements a three-layer feed-forward neural network built using a back-propagation learning technique that is based on the gradient descent rule. We analyzed the massradius relations and the density profiles of the relativistic isothermal gas spheres against different relativistic parameters and compared the ANN solutions with the analytical ones. The comparison between the two solutions reflects the efficiency of using the ANN to solve TOV equations.","PeriodicalId":49602,"journal":{"name":"Revista Mexicana de Astronomia y Astrofisica","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ANN AND ANALYTICAL SOLUTIONS TO RELATIVISTIC ISOTHERMAL GAS SPHERES\",\"authors\":\"M. Nouh, Y. A. Azzam, E. Abdel-salam, F. Elnagahy, T. M. Kamel\",\"doi\":\"10.22201/ia.01851101p.2022.58.02.13\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Relativistic isothermal gas spheres are a powerful tool to model many astronomical objects, like compact stars and clusters of galaxies. In the present paper, we introduce an artificial neural network (ANN) algorithm and Taylor series to model the relativistic gas spheres using Tolman-Oppenheimer-Volkoff differential equations (TOV). Comparing the analytical solutions with the numerical ones revealed good agreement with maximum relative errors of 10−3. The ANN algorithm implements a three-layer feed-forward neural network built using a back-propagation learning technique that is based on the gradient descent rule. We analyzed the massradius relations and the density profiles of the relativistic isothermal gas spheres against different relativistic parameters and compared the ANN solutions with the analytical ones. The comparison between the two solutions reflects the efficiency of using the ANN to solve TOV equations.\",\"PeriodicalId\":49602,\"journal\":{\"name\":\"Revista Mexicana de Astronomia y Astrofisica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Mexicana de Astronomia y Astrofisica\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.22201/ia.01851101p.2022.58.02.13\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Mexicana de Astronomia y Astrofisica","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.22201/ia.01851101p.2022.58.02.13","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}

引用次数: 0

摘要

相对论等温气体球是模拟许多天体的强大工具，比如致密恒星和星系团。在本文中，我们引入了一种人工神经网络（ANN）算法和泰勒级数，使用Tolman-Openheimer-Volkoff微分方程（TOV）对相对论性气体球进行建模。将解析解与数值解进行比较，结果表明，最大相对误差为10−3。ANN算法实现了一个三层前馈神经网络，该网络使用基于梯度下降规则的反向传播学习技术构建。我们分析了相对论等温气体球在不同相对论参数下的质量半径关系和密度分布，并将ANN解与解析解进行了比较。两种解之间的比较反映了使用人工神经网络求解TOV方程的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

ANN AND ANALYTICAL SOLUTIONS TO RELATIVISTIC ISOTHERMAL GAS SPHERES

Relativistic isothermal gas spheres are a powerful tool to model many astronomical objects, like compact stars and clusters of galaxies. In the present paper, we introduce an artificial neural network (ANN) algorithm and Taylor series to model the relativistic gas spheres using Tolman-Oppenheimer-Volkoff differential equations (TOV). Comparing the analytical solutions with the numerical ones revealed good agreement with maximum relative errors of 10−3. The ANN algorithm implements a three-layer feed-forward neural network built using a back-propagation learning technique that is based on the gradient descent rule. We analyzed the massradius relations and the density profiles of the relativistic isothermal gas spheres against different relativistic parameters and compared the ANN solutions with the analytical ones. The comparison between the two solutions reflects the efficiency of using the ANN to solve TOV equations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Revista Mexicana de Astronomia y Astrofisica 地学天文-天文与天体物理

CiteScore

1.30

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Revista Mexicana de Astronomía y Astrofísica, founded in 1974, publishes original research papers in all branches of astronomy, astrophysics and closely related fields. Two numbers per year are issued and are distributed free of charge to all institutions engaged in the fields covered by the RMxAA.