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IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/24m1691454
The Editors
{"title":"SIGEST","authors":"The Editors","doi":"10.1137/24m1691454","DOIUrl":"https://doi.org/10.1137/24m1691454","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 105-105, March 2025. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"78 1 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Featured Review:; Numerical Integration of Differential Equations 评论:;微分方程的数值积分
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/24m1678684
John C. Butcher, Robert M. Corless
{"title":"Featured Review:; Numerical Integration of Differential Equations","authors":"John C. Butcher, Robert M. Corless","doi":"10.1137/24m1678684","DOIUrl":"https://doi.org/10.1137/24m1678684","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 197-204, March 2025. <br/> The book under review was originally published under the auspices of the National Research Council in 1933 (the year John was born), and it was republished as a Dover edition in 1956 (three years before Rob was born). At 108 pages—including title page, preface, table of contents, and index—it’s very short. Even so, it contains a significant amount of information that was of technical importance for its time and is of historical importance now.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"14 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Graph Neural Networks and Applied Linear Algebra 图神经网络与应用线性代数
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/23m1609786
Nicholas S. Moore, Eric C. Cyr, Peter Ohm, Christopher M. Siefert, Raymond S. Tuminaro
{"title":"Graph Neural Networks and Applied Linear Algebra","authors":"Nicholas S. Moore, Eric C. Cyr, Peter Ohm, Christopher M. Siefert, Raymond S. Tuminaro","doi":"10.1137/23m1609786","DOIUrl":"https://doi.org/10.1137/23m1609786","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 141-175, March 2025. <br/> Abstract.Sparse matrix computations are ubiquitous in scientific computing. Given the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NNs). Unfortunately, multilayer perceptron (MLP) NNs are typically not natural for either graph or sparse matrix computations. The issue lies with the fact that MLPs require fixed-sized inputs, while scientific applications generally generate sparse matrices with arbitrary dimensions and a wide range of different nonzero patterns (or matrix graph vertex interconnections). While convolutional NNs could possibly address matrix graphs where all vertices have the same number of nearest neighbors, a more general approach is needed for arbitrary sparse matrices, e.g., those arising from discretized partial differential equations on unstructured meshes. Graph neural networks (GNNs) are one such approach suitable to sparse matrices. The key idea is to define aggregation functions (e.g., summations) that operate on variable-size input data to produce data of a fixed output size so that MLPs can be applied. The goal of this paper is to provide an introduction to GNNs for a numerical linear algebra audience. Concrete GNN examples are provided to illustrate how many common linear algebra tasks can be accomplished using GNNs. We focus on iterative and multigrid methods that employ computational kernels such as matrix-vector products, interpolation, relaxation methods, and strength-of-connection measures. Our GNN examples include cases where parameters are determined a priori as well as cases where parameters must be learned. The intent of this paper is to help computational scientists understand how GNNs can be used to adapt machine learning concepts to computational tasks associated with sparse matrices. It is hoped that this understanding will further stimulate data-driven extensions of classical sparse linear algebra tasks.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"40 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Book Review:; Probability Adventures 书评:;概率的冒险
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/24m1646108
Nevena Marić
{"title":"Book Review:; Probability Adventures","authors":"Nevena Marić","doi":"10.1137/24m1646108","DOIUrl":"https://doi.org/10.1137/24m1646108","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 205-206, March 2025. <br/> The first look at Probability Adventures brought back memories of a conference in Ubatuba, Brazil, in 2001, where as a young Master’s student I worried that true science had to be deadly serious. Fortunately, several inspiring teachers came to the rescue. Andrei Toom’s words resonated deeply with me when he began his lecture by saying, “Every mathematician is a big child.” The esteemed audience beamed with approval. Today, I look at Probability Adventures and applaud Mark Huber for honoring the child in all of us and offering a reading that is both fun and mathematically rigorous.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"45 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Book Review:; Elegant Simulations. From Simple Oscillators to Many-Body Systems 书评:;优雅的模拟。从简单振荡器到多体系统
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/24m1690953
Omar Morandi
{"title":"Book Review:; Elegant Simulations. From Simple Oscillators to Many-Body Systems","authors":"Omar Morandi","doi":"10.1137/24m1690953","DOIUrl":"https://doi.org/10.1137/24m1690953","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 207-208, March 2025. <br/> Elegant Simulations covers various aspects of modeling and simulating mechanical systems described at the elementary level by many-interacting particles. The book presents the topics from an original and fresh point of view. The complex many-body dynamics is reproduced at the elementary level in terms of simple models that are easy to understand and interpret. The principal benefit for the reader is that this approach helps to develop an intuitive picture of the complex many-body dynamics.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"11 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Risk-Adaptive Approaches to Stochastic Optimization: A Survey 随机优化的风险自适应方法综述
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/22m1538946
Johannes O. Royset
{"title":"Risk-Adaptive Approaches to Stochastic Optimization: A Survey","authors":"Johannes O. Royset","doi":"10.1137/22m1538946","DOIUrl":"https://doi.org/10.1137/22m1538946","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 3-70, March 2025. <br/> Abstract.Uncertainty is prevalent in engineering design and data-driven problems and, more broadly, in decision making. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey the rapid development of risk measures over the last quarter century. From their beginning in financial engineering, we recount their spread to nearly all areas of engineering and applied mathematics. Solidly rooted in convex analysis, risk measures furnish a general framework for handling uncertainty with significant computational and theoretical advantages. We describe the key facts, list several concrete algorithms, and provide an extensive list of references for further reading. The survey recalls connections with utility theory and distributionally robust optimization, points to emerging applications areas such as fair machine learning, and defines measures of reliability.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"128 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Neighborhood Watch in Mechanics: Nonlocal Models and Convolution 力学中的邻域监视：非局部模型和卷积
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/22m1541721
Thomas Nagel, Tymofiy Gerasimov, Jere Remes, Dominik Kern
{"title":"Neighborhood Watch in Mechanics: Nonlocal Models and Convolution","authors":"Thomas Nagel, Tymofiy Gerasimov, Jere Remes, Dominik Kern","doi":"10.1137/22m1541721","DOIUrl":"https://doi.org/10.1137/22m1541721","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 176-193, March 2025. <br/> Abstract.This paper is intended to serve as a low-hurdle introduction to nonlocality for graduate students and researchers with an engineering mechanics or physics background who did not have a formal introduction to the underlying mathematical basis. We depart from simple examples motivated by structural mechanics to form a physical intuition and demonstrate nonlocality using concepts familiar to most engineers. We then show how concepts of nonlocality are at the core of one of the most active current research fields in applied mechanics, namely, in phase-field modeling of fracture. From a mathematical perspective, these developments rest on the concept of convolution in both its discrete and its continuous forms. The previous mechanical examples may thus serve as an intuitive explanation of what convolution implies from a physical perspective. In the supplementary material we highlight a broader range of applications of the concepts of nonlocality and convolution in other branches of science and engineering by generalizing from the examples explained in detail in the main body of the article.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"47 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Survey and Review 调查及检讨
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/24m1691430
Marlis Hochbruck
{"title":"Survey and Review","authors":"Marlis Hochbruck","doi":"10.1137/24m1691430","DOIUrl":"https://doi.org/10.1137/24m1691430","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 1-1, March 2025. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"20 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Book Review:; Mathematical Pictures at a Data Science Exhibition 书评:;数据科学展览中的数学图片
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/24m1635077
Bamdad Hosseini
{"title":"Book Review:; Mathematical Pictures at a Data Science Exhibition","authors":"Bamdad Hosseini","doi":"10.1137/24m1635077","DOIUrl":"https://doi.org/10.1137/24m1635077","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 208-209, March 2025. <br/> The book Mathematical Pictures at a Data Science Exhibition aims to introduce the reader to the many mathematical ideas that congregate under the ever-expanding umbrella of data science. Given the meteoric rise of this field and the immense speed at which it often moves, this book acts as a welcome road map for graduate students and researchers in the field. Given its focus on theory, the book should be most appreciated by mathematicians as well as theoretical statisticians and computer scientists. While algorithms are the main focus of the book, the exposition is by no means a hands-on tutorial in data science, but rather an introductory text on the theoretical ideas behind data science algorithms and problems.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"11 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Education 教育
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-02-06 DOI: 10.1137/24m1691478
Hélène Frankowska
{"title":"Education","authors":"Hélène Frankowska","doi":"10.1137/24m1691478","DOIUrl":"https://doi.org/10.1137/24m1691478","url":null,"abstract":"SIAM Review, Volume 67, Issue 1, Page 139-140, March 2025. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"13 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143258455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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