基于 Neumann 序列的神经算子用于解决逆介质问题

Ziyang Liu, Fukai Chen, Junqing Chen, Lingyun Qiu, Zuoqiang Shi
{"title":"基于 Neumann 序列的神经算子用于解决逆介质问题","authors":"Ziyang Liu, Fukai Chen, Junqing Chen, Lingyun Qiu, Zuoqiang Shi","doi":"arxiv-2409.09480","DOIUrl":null,"url":null,"abstract":"The inverse medium problem, inherently ill-posed and nonlinear, presents\nsignificant computational challenges. This study introduces a novel approach by\nintegrating a Neumann series structure within a neural network framework to\neffectively handle multiparameter inputs. Experiments demonstrate that our\nmethodology not only accelerates computations but also significantly enhances\ngeneralization performance, even with varying scattering properties and noisy\ndata. The robustness and adaptability of our framework provide crucial insights\nand methodologies, extending its applicability to a broad spectrum of\nscattering problems. These advancements mark a significant step forward in the\nfield, offering a scalable solution to traditionally complex inverse problems.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Neumann Series-based Neural Operator for Solving Inverse Medium Problem\",\"authors\":\"Ziyang Liu, Fukai Chen, Junqing Chen, Lingyun Qiu, Zuoqiang Shi\",\"doi\":\"arxiv-2409.09480\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The inverse medium problem, inherently ill-posed and nonlinear, presents\\nsignificant computational challenges. This study introduces a novel approach by\\nintegrating a Neumann series structure within a neural network framework to\\neffectively handle multiparameter inputs. Experiments demonstrate that our\\nmethodology not only accelerates computations but also significantly enhances\\ngeneralization performance, even with varying scattering properties and noisy\\ndata. The robustness and adaptability of our framework provide crucial insights\\nand methodologies, extending its applicability to a broad spectrum of\\nscattering problems. These advancements mark a significant step forward in the\\nfield, offering a scalable solution to traditionally complex inverse problems.\",\"PeriodicalId\":501312,\"journal\":{\"name\":\"arXiv - MATH - Mathematical Physics\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09480\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09480","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

逆介质问题本质上是一个求解困难的非线性问题,给计算带来了巨大挑战。本研究引入了一种新方法,在神经网络框架内整合了诺依曼数列结构,以有效处理多参数输入。实验证明,我们的方法不仅加快了计算速度,还显著提高了泛化性能,即使在散射特性和噪声数据各不相同的情况下也是如此。我们框架的鲁棒性和适应性提供了重要的洞察力和方法论,使其适用于广泛的散射问题。这些进步标志着该领域向前迈出了重要一步,为传统的复杂逆问题提供了可扩展的解决方案。
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
Neumann Series-based Neural Operator for Solving Inverse Medium Problem
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively handle multiparameter inputs. Experiments demonstrate that our methodology not only accelerates computations but also significantly enhances generalization performance, even with varying scattering properties and noisy data. The robustness and adaptability of our framework provide crucial insights and methodologies, extending its applicability to a broad spectrum of scattering problems. These advancements mark a significant step forward in the field, offering a scalable solution to traditionally complex inverse problems.
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
自引率
0.00%
发文量
0
期刊最新文献
Analysis of a Mathematical Model for Fluid Transport in Poroelastic Materials in 2D Space Determination of Fisher and Shannon Information for 1D Fractional Quantum Harmonic Oscillator Drinfel'd Doubles, Twists and All That... in Stringy Geometry and M Theory Integrable dynamics from Fermat's principle A comparison between classical and Bohmian quantum chaos
×
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