chebgreen:从数据中学习和插值连续经验格林函数

IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Harshwardhan Praveen , Jacob Brown , Christopher Earls
{"title":"chebgreen:从数据中学习和插值连续经验格林函数","authors":"Harshwardhan Praveen ,&nbsp;Jacob Brown ,&nbsp;Christopher Earls","doi":"10.1016/j.cpc.2025.109867","DOIUrl":null,"url":null,"abstract":"<div><div>In this work, we present a mesh-independent, data-driven library, <span>chebgreen</span>, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is <em>unknown</em>. The proposed method learns an Empirical Green's Function for the associated, but hidden, boundary value problem, in the form of a Rational Neural Network from which we subsequently construct a bivariate representation in a Chebyshev basis. We uncover the Green's function, at an unseen control parameter value, by interpolating the left and right singular functions within a suitable library, expressed as points on a manifold of Quasimatrices, while the associated singular values are interpolated with Lagrange polynomials. This work improves upon prior work by extending the scope of applicability to non-self-adjoint operators and improves data efficiency.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"317 ","pages":"Article 109867"},"PeriodicalIF":3.4000,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"chebgreen: Learning and interpolating continuous Empirical Green's Functions from data\",\"authors\":\"Harshwardhan Praveen ,&nbsp;Jacob Brown ,&nbsp;Christopher Earls\",\"doi\":\"10.1016/j.cpc.2025.109867\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this work, we present a mesh-independent, data-driven library, <span>chebgreen</span>, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is <em>unknown</em>. The proposed method learns an Empirical Green's Function for the associated, but hidden, boundary value problem, in the form of a Rational Neural Network from which we subsequently construct a bivariate representation in a Chebyshev basis. We uncover the Green's function, at an unseen control parameter value, by interpolating the left and right singular functions within a suitable library, expressed as points on a manifold of Quasimatrices, while the associated singular values are interpolated with Lagrange polynomials. This work improves upon prior work by extending the scope of applicability to non-self-adjoint operators and improves data efficiency.</div></div>\",\"PeriodicalId\":285,\"journal\":{\"name\":\"Computer Physics Communications\",\"volume\":\"317 \",\"pages\":\"Article 109867\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2025-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Physics Communications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0010465525003698\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465525003698","RegionNum":2,"RegionCategory":"物理与天体物理","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

摘要

在这项工作中,我们提出了一个网格独立的数据驱动库chebgreen,用于对一维系统进行数学建模,该系统具有相关的控制参数,其控制偏微分方程未知。提出的方法为相关的,但隐藏的,边值问题学习一个经验格林函数,以一个理性神经网络的形式,我们随后在切比雪夫基中构造一个二元表示。我们在一个不可见的控制参数值下,通过在一个合适的库内插值左、右奇异函数来揭示格林函数,这些函数表示为拟矩阵流形上的点,而相关的奇异值则用拉格朗日多项式插值。这项工作通过将适用范围扩展到非自伴随算子来改进先前的工作,并提高了数据效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
chebgreen: Learning and interpolating continuous Empirical Green's Functions from data
In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The proposed method learns an Empirical Green's Function for the associated, but hidden, boundary value problem, in the form of a Rational Neural Network from which we subsequently construct a bivariate representation in a Chebyshev basis. We uncover the Green's function, at an unseen control parameter value, by interpolating the left and right singular functions within a suitable library, expressed as points on a manifold of Quasimatrices, while the associated singular values are interpolated with Lagrange polynomials. This work improves upon prior work by extending the scope of applicability to non-self-adjoint operators and improves data 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
Computer Physics Communications
Computer Physics Communications 物理-计算机:跨学科应用
CiteScore
12.10
自引率
3.20%
发文量
287
审稿时长
5.3 months
期刊介绍: The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信