用于正演和反演 PDE 问题的深度模糊物理信息神经网络。

IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Neural Networks Pub Date : 2024-10-15 DOI:10.1016/j.neunet.2024.106750
Wenyuan Wu , Siyuan Duan , Yuan Sun , Yang Yu , Dong Liu , Dezhong Peng
{"title":"用于正演和反演 PDE 问题的深度模糊物理信息神经网络。","authors":"Wenyuan Wu ,&nbsp;Siyuan Duan ,&nbsp;Yuan Sun ,&nbsp;Yang Yu ,&nbsp;Dong Liu ,&nbsp;Dezhong Peng","doi":"10.1016/j.neunet.2024.106750","DOIUrl":null,"url":null,"abstract":"<div><div>As a grid-independent approach for solving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have garnered significant attention due to their unique capability to simultaneously learn from both data and the governing physical equations. Existing PINNs methods always assume that the data is stable and reliable, but data obtained from commercial simulation software often inevitably have ambiguous and inaccurate problems. Obviously, this will have a negative impact on the use of PINNs to solve forward and inverse PDE problems. To overcome the above problems, this paper proposes a Deep Fuzzy Physics-Informed Neural Networks (FPINNs) that explores the uncertainty in data. Specifically, to capture the uncertainty behind the data, FPINNs learns fuzzy representation through the fuzzy membership function layer and fuzzy rule layer. Afterward, we use deep neural networks to learn neural representation. Subsequently, the fuzzy representation is integrated with the neural representation. Finally, the residual of the physical equation and the data error are considered as the two components of the loss function, guiding the network to optimize towards adherence to the physical laws for accurate prediction of the physical field. Extensive experiment results show that FPINNs outperforms these comparative methods in solving forward and inverse PDE problems on four widely used datasets. The demo code will be released at <span><span>https://github.com/siyuancncd/FPINNs</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":49763,"journal":{"name":"Neural Networks","volume":"181 ","pages":"Article 106750"},"PeriodicalIF":6.0000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Deep fuzzy physics-informed neural networks for forward and inverse PDE problems\",\"authors\":\"Wenyuan Wu ,&nbsp;Siyuan Duan ,&nbsp;Yuan Sun ,&nbsp;Yang Yu ,&nbsp;Dong Liu ,&nbsp;Dezhong Peng\",\"doi\":\"10.1016/j.neunet.2024.106750\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>As a grid-independent approach for solving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have garnered significant attention due to their unique capability to simultaneously learn from both data and the governing physical equations. Existing PINNs methods always assume that the data is stable and reliable, but data obtained from commercial simulation software often inevitably have ambiguous and inaccurate problems. Obviously, this will have a negative impact on the use of PINNs to solve forward and inverse PDE problems. To overcome the above problems, this paper proposes a Deep Fuzzy Physics-Informed Neural Networks (FPINNs) that explores the uncertainty in data. Specifically, to capture the uncertainty behind the data, FPINNs learns fuzzy representation through the fuzzy membership function layer and fuzzy rule layer. Afterward, we use deep neural networks to learn neural representation. Subsequently, the fuzzy representation is integrated with the neural representation. Finally, the residual of the physical equation and the data error are considered as the two components of the loss function, guiding the network to optimize towards adherence to the physical laws for accurate prediction of the physical field. Extensive experiment results show that FPINNs outperforms these comparative methods in solving forward and inverse PDE problems on four widely used datasets. The demo code will be released at <span><span>https://github.com/siyuancncd/FPINNs</span><svg><path></path></svg></span>.</div></div>\",\"PeriodicalId\":49763,\"journal\":{\"name\":\"Neural Networks\",\"volume\":\"181 \",\"pages\":\"Article 106750\"},\"PeriodicalIF\":6.0000,\"publicationDate\":\"2024-10-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Neural Networks\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893608024006749\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neural Networks","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893608024006749","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0

摘要

物理信息神经网络(PINNs)是一种独立于网格的偏微分方程(PDEs)求解方法,因其同时从数据和物理方程中学习的独特能力而备受关注。现有的 PINNs 方法总是假定数据是稳定可靠的,但从商业模拟软件中获得的数据往往不可避免地存在模糊和不准确的问题。显然,这将对使用 PINNs 解决正演和反演 PDE 问题产生负面影响。为了克服上述问题,本文提出了一种探索数据不确定性的深度模糊物理信息神经网络(FPINNs)。具体来说,为了捕捉数据背后的不确定性,FPINNs 通过模糊成员函数层和模糊规则层学习模糊表示。之后,我们使用深度神经网络来学习神经表征。随后,将模糊表示与神经表示进行整合。最后,物理方程的残差和数据误差被视为损失函数的两个分量,引导网络朝着遵循物理规律的方向进行优化,从而实现对物理场的精确预测。广泛的实验结果表明,在解决四个广泛使用的数据集上的正演和反演 PDE 问题时,FPINNs 优于这些比较方法。演示代码将在 https://github.com/siyuancncd/FPINNs 上发布。
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
Deep fuzzy physics-informed neural networks for forward and inverse PDE problems
As a grid-independent approach for solving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have garnered significant attention due to their unique capability to simultaneously learn from both data and the governing physical equations. Existing PINNs methods always assume that the data is stable and reliable, but data obtained from commercial simulation software often inevitably have ambiguous and inaccurate problems. Obviously, this will have a negative impact on the use of PINNs to solve forward and inverse PDE problems. To overcome the above problems, this paper proposes a Deep Fuzzy Physics-Informed Neural Networks (FPINNs) that explores the uncertainty in data. Specifically, to capture the uncertainty behind the data, FPINNs learns fuzzy representation through the fuzzy membership function layer and fuzzy rule layer. Afterward, we use deep neural networks to learn neural representation. Subsequently, the fuzzy representation is integrated with the neural representation. Finally, the residual of the physical equation and the data error are considered as the two components of the loss function, guiding the network to optimize towards adherence to the physical laws for accurate prediction of the physical field. Extensive experiment results show that FPINNs outperforms these comparative methods in solving forward and inverse PDE problems on four widely used datasets. The demo code will be released at https://github.com/siyuancncd/FPINNs.
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. Corrigendum to "Multi-view Graph Pooling with Coarsened Graph Disentanglement" [Neural Networks 174 (2024) 1-10/106221]. Multi-compartment neuron and population encoding powered spiking neural network for deep distributional reinforcement learning. Multiscroll hopfield neural network with extreme multistability and its application in video encryption for IIoT.
×
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