用于解决正向和反向动态问题的频谱集成神经网络(SINNs)。

IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Neural Networks Pub Date : 2024-12-01 Epub Date: 2024-09-22 DOI:10.1016/j.neunet.2024.106756
Lin Qiu, Fajie Wang, Wenzhen Qu, Yan Gu, Qing-Hua Qin
{"title":"用于解决正向和反向动态问题的频谱集成神经网络(SINNs)。","authors":"Lin Qiu, Fajie Wang, Wenzhen Qu, Yan Gu, Qing-Hua Qin","doi":"10.1016/j.neunet.2024.106756","DOIUrl":null,"url":null,"abstract":"<p><p>This study introduces an innovative neural network framework named spectral integrated neural networks (SINNs) to address both forward and inverse dynamic problems in three-dimensional space. In the SINNs, the spectral integration technique is utilized for temporal discretization, followed by the application of a fully connected neural network to solve the resulting partial differential equations in the spatial domain. Furthermore, the polynomial basis functions are employed to expand the unknown function, with the goal of improving the performance of SINNs in tackling inverse problems. The performance of the developed framework is evaluated through several dynamic benchmark examples encompassing linear and nonlinear heat conduction problems, linear and nonlinear wave propagation problems, inverse problem of heat conduction, and long-time heat conduction problem. The numerical results demonstrate that the SINNs can effectively and accurately solve forward and inverse problems involving heat conduction and wave propagation. Additionally, the SINNs provide precise and stable solutions for dynamic problems with extended time durations. Compared to commonly used physics-informed neural networks, the SINNs exhibit superior performance with enhanced convergence speed, computational accuracy, and efficiency.</p>","PeriodicalId":49763,"journal":{"name":"Neural Networks","volume":null,"pages":null},"PeriodicalIF":6.0000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems.\",\"authors\":\"Lin Qiu, Fajie Wang, Wenzhen Qu, Yan Gu, Qing-Hua Qin\",\"doi\":\"10.1016/j.neunet.2024.106756\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>This study introduces an innovative neural network framework named spectral integrated neural networks (SINNs) to address both forward and inverse dynamic problems in three-dimensional space. In the SINNs, the spectral integration technique is utilized for temporal discretization, followed by the application of a fully connected neural network to solve the resulting partial differential equations in the spatial domain. Furthermore, the polynomial basis functions are employed to expand the unknown function, with the goal of improving the performance of SINNs in tackling inverse problems. The performance of the developed framework is evaluated through several dynamic benchmark examples encompassing linear and nonlinear heat conduction problems, linear and nonlinear wave propagation problems, inverse problem of heat conduction, and long-time heat conduction problem. The numerical results demonstrate that the SINNs can effectively and accurately solve forward and inverse problems involving heat conduction and wave propagation. Additionally, the SINNs provide precise and stable solutions for dynamic problems with extended time durations. Compared to commonly used physics-informed neural networks, the SINNs exhibit superior performance with enhanced convergence speed, computational accuracy, and efficiency.</p>\",\"PeriodicalId\":49763,\"journal\":{\"name\":\"Neural Networks\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.0000,\"publicationDate\":\"2024-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Neural Networks\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1016/j.neunet.2024.106756\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/9/22 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neural Networks","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1016/j.neunet.2024.106756","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/9/22 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0

摘要

本研究介绍了一种名为光谱集成神经网络(SINNs)的创新神经网络框架,用于解决三维空间中的正向和反向动态问题。在 SINNs 中,利用频谱积分技术进行时间离散化,然后应用全连接神经网络求解空间域的偏微分方程。此外,还采用多项式基函数来扩展未知函数,目的是提高 SINN 在处理逆问题时的性能。通过几个动态基准示例,包括线性和非线性热传导问题、线性和非线性波传播问题、热传导逆问题和长时间热传导问题,对所开发框架的性能进行了评估。数值结果表明,SINN 可以有效、准确地解决涉及热传导和波传播的正向和反向问题。此外,SINN 还能为时间持续较长的动态问题提供精确而稳定的解决方案。与常用的物理信息神经网络相比,SINN 在收敛速度、计算精度和效率方面表现出更优越的性能。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems.

This study introduces an innovative neural network framework named spectral integrated neural networks (SINNs) to address both forward and inverse dynamic problems in three-dimensional space. In the SINNs, the spectral integration technique is utilized for temporal discretization, followed by the application of a fully connected neural network to solve the resulting partial differential equations in the spatial domain. Furthermore, the polynomial basis functions are employed to expand the unknown function, with the goal of improving the performance of SINNs in tackling inverse problems. The performance of the developed framework is evaluated through several dynamic benchmark examples encompassing linear and nonlinear heat conduction problems, linear and nonlinear wave propagation problems, inverse problem of heat conduction, and long-time heat conduction problem. The numerical results demonstrate that the SINNs can effectively and accurately solve forward and inverse problems involving heat conduction and wave propagation. Additionally, the SINNs provide precise and stable solutions for dynamic problems with extended time durations. Compared to commonly used physics-informed neural networks, the SINNs exhibit superior performance with enhanced convergence speed, computational accuracy, and efficiency.

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
Neural Networks
Neural Networks 工程技术-计算机:人工智能
CiteScore
13.90
自引率
7.70%
发文量
425
审稿时长
67 days
期刊介绍: Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.
期刊最新文献
Multi-source Selective Graph Domain Adaptation Network for cross-subject EEG emotion recognition. Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems. Deep Incomplete Multi-view Clustering via Multi-level Imputation and Contrastive Alignment. Tensorial multiview low-rank high-order graph learning for context-enhanced domain adaptation. Multi-focus image fusion with parameter adaptive dual channel dynamic threshold neural P systems.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1