Partial Differential Equations Meet Deep Neural Networks: A Survey.

IF 10.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE IEEE transactions on neural networks and learning systems Pub Date : 2025-03-14 DOI:10.1109/TNNLS.2025.3545967
Shudong Huang, Wentao Feng, Chenwei Tang, Zhenan He, Caiyang Yu, Jiancheng Lv
{"title":"Partial Differential Equations Meet Deep Neural Networks: A Survey.","authors":"Shudong Huang, Wentao Feng, Chenwei Tang, Zhenan He, Caiyang Yu, Jiancheng Lv","doi":"10.1109/TNNLS.2025.3545967","DOIUrl":null,"url":null,"abstract":"<p><p>Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), molecular dynamics, and dynamical systems. Although traditional numerical methods like the finite difference/element method are widely used, their computational inefficiency, due to the large number of iterations required, has long been a challenge. Recently, deep learning (DL) has emerged as a promising alternative for solving PDEs, offering new paradigms beyond conventional methods. Despite the growing interest in techniques like physics-informed neural networks (PINNs), a systematic review of the diverse neural network (NN) approaches for PDEs is still missing. This survey fills that gap by categorizing and reviewing the current progress of deep NNs (DNNs) for PDEs. Unlike previous reviews focused on specific methods like PINNs, we offer a broader taxonomy and analyze applications across scientific, engineering, and medical fields. We also provide a historical overview, key challenges, and future trends, aiming to serve both researchers and practitioners with insights into how DNNs can be effectively applied to solve PDEs.</p>","PeriodicalId":13303,"journal":{"name":"IEEE transactions on neural networks and learning systems","volume":"PP ","pages":""},"PeriodicalIF":10.2000,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE transactions on neural networks and learning systems","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1109/TNNLS.2025.3545967","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

Abstract

Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), molecular dynamics, and dynamical systems. Although traditional numerical methods like the finite difference/element method are widely used, their computational inefficiency, due to the large number of iterations required, has long been a challenge. Recently, deep learning (DL) has emerged as a promising alternative for solving PDEs, offering new paradigms beyond conventional methods. Despite the growing interest in techniques like physics-informed neural networks (PINNs), a systematic review of the diverse neural network (NN) approaches for PDEs is still missing. This survey fills that gap by categorizing and reviewing the current progress of deep NNs (DNNs) for PDEs. Unlike previous reviews focused on specific methods like PINNs, we offer a broader taxonomy and analyze applications across scientific, engineering, and medical fields. We also provide a historical overview, key challenges, and future trends, aiming to serve both researchers and practitioners with insights into how DNNs can be effectively applied to solve PDEs.

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
偏微分方程与深度神经网络相遇:调查。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
IEEE transactions on neural networks and learning systems
IEEE transactions on neural networks and learning systems COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, HARDWARE & ARCHITECTURE
CiteScore
23.80
自引率
9.60%
发文量
2102
审稿时长
3-8 weeks
期刊介绍: The focus of IEEE Transactions on Neural Networks and Learning Systems is to present scholarly articles discussing the theory, design, and applications of neural networks as well as other learning systems. The journal primarily highlights technical and scientific research in this domain.
期刊最新文献
INGC-GAN: An Implicit Neural-Guided Cycle Generative Approach for Perceptual-Friendly Underwater Image Enhancement. Neuron Perception Inspired EEG Emotion Recognition With Parallel Contrastive Learning. NiSNN-A: Noniterative Spiking Neural Network With Attention With Application to Motor Imagery EEG Classification. Partial Differential Equations Meet Deep Neural Networks: A Survey. Provably Bounded Dynamic Sparsifying Transform Network for Compressive Imaging.
×
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