Promising directions of machine learning for partial differential equations

IF 12 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Nature computational science Pub Date : 2024-06-28 DOI:10.1038/s43588-024-00643-2
Steven L. Brunton, J. Nathan Kutz
{"title":"Promising directions of machine learning for partial differential equations","authors":"Steven L. Brunton, J. Nathan Kutz","doi":"10.1038/s43588-024-00643-2","DOIUrl":null,"url":null,"abstract":"Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multiscale physics in a compact and symbolic representation. Here, we examine several promising avenues of PDE research that are being advanced by machine learning, including (1) discovering new governing PDEs and coarse-grained approximations for complex natural and engineered systems, (2) learning effective coordinate systems and reduced-order models to make PDEs more amenable to analysis, and (3) representing solution operators and improving traditional numerical algorithms. In each of these fields, we summarize key advances, ongoing challenges, and opportunities for further development. Machine learning has enabled major advances in the field of partial differential equations. This Review discusses some of these efforts and other ongoing challenges and opportunities for development.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":null,"pages":null},"PeriodicalIF":12.0000,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nature computational science","FirstCategoryId":"1085","ListUrlMain":"https://www.nature.com/articles/s43588-024-00643-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

Abstract

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multiscale physics in a compact and symbolic representation. Here, we examine several promising avenues of PDE research that are being advanced by machine learning, including (1) discovering new governing PDEs and coarse-grained approximations for complex natural and engineered systems, (2) learning effective coordinate systems and reduced-order models to make PDEs more amenable to analysis, and (3) representing solution operators and improving traditional numerical algorithms. In each of these fields, we summarize key advances, ongoing challenges, and opportunities for further development. Machine learning has enabled major advances in the field of partial differential equations. This Review discusses some of these efforts and other ongoing challenges and opportunities for development.

Abstract Image

Abstract Image

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
偏微分方程机器学习的发展方向。
偏微分方程(PDEs)是对自然物理规律最通用、最简洁的描述之一,它以紧凑的符号表示捕捉了丰富多样的现象学和多尺度物理学。在此,我们将探讨机器学习正在推动的几种有前途的多导方程研究途径,包括:(1) 为复杂的自然和工程系统发现新的支配多导方程和粗粒度近似值;(2) 学习有效坐标系和降阶模型,使多导方程更易于分析;(3) 表示求解算子并改进传统的数值算法。在上述每个领域,我们都总结了主要进展、当前挑战和进一步发展的机遇。
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
CiteScore
11.70
自引率
0.00%
发文量
0
期刊最新文献
Real-time non-line-of-sight computational imaging using spectrum filtering and motion compensation. Deep generative design of RNA aptamers using structural predictions. Extracting reliable quantum outputs for noisy devices. Provable bounds for noise-free expectation values computed from noisy samples. E-waste challenges of generative artificial intelligence.
×
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