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Stochastic Dual Dynamic Programming and Its Variants: A Review 随机对偶动态规划及其变体综述
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/23m1575093
Christian Füllner, Steffen Rebennack
{"title":"Stochastic Dual Dynamic Programming and Its Variants: A Review","authors":"Christian Füllner, Steffen Rebennack","doi":"10.1137/23m1575093","DOIUrl":"https://doi.org/10.1137/23m1575093","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 415-539, August 2025. <br/> Abstract.We provide a tutorial-style review of stochastic dual dynamic programming (SDDP), one of the state-of-the-art solution methods for large-scale multistage stochastic programs. Since it was introduced about 30 years ago for solving large-scale multistage stochastic linear programming problems in energy planning, SDDP has been applied to practical problems from several fields and has been enriched by various improvements and enhancements to address broader problem classes. We begin with a detailed introduction to SDDP, with special focus on its motivation, complexity, and required assumptions. Then, we present and discuss in depth the existing enhancements as well as current research trends that allow for the alleviation of those assumptions.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"16 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144797304","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 : 2025-08-07 DOI: 10.1137/25m1741479
Hélène Frankowska
{"title":"Education","authors":"Hélène Frankowska","doi":"10.1137/25m1741479","DOIUrl":"https://doi.org/10.1137/25m1741479","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 605-605, August 2025. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"31 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792619","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 : 2025-08-07 DOI: 10.1137/25m1741455
Marlis Hochbruck
{"title":"Survey and Review","authors":"Marlis Hochbruck","doi":"10.1137/25m1741455","DOIUrl":"https://doi.org/10.1137/25m1741455","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 413-413, August 2025. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"734 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792668","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:; Statistical Foundations of Actuarial Learning and Its Applications 书评:;精算学习的统计基础及其应用
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/24m1651575
Olivier Menoukeu-Pamen
{"title":"Book Review:; Statistical Foundations of Actuarial Learning and Its Applications","authors":"Olivier Menoukeu-Pamen","doi":"10.1137/24m1651575","DOIUrl":"https://doi.org/10.1137/24m1651575","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 656-658, August 2025. <br/> In insurance mathematics and actuarial sciences, modeling the dynamics of insured events is a pivotal challenge that demands advanced and sophisticated techniques due to the growing complexity of insurance markets. This complexity, coupled with the exponential growth in data availability in recent years, has acted as a catalyst for the adoption of datacentric approaches in forecasting random phenomena.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"27 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792665","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
Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs 建模仍然很重要：数学生物学中灾难性浮点错误的一个令人惊讶的实例和ode的数值方法
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/23m1563967
Cordula Reisch, Hendrik Ranocha
{"title":"Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs","authors":"Cordula Reisch, Hendrik Ranocha","doi":"10.1137/23m1563967","DOIUrl":"https://doi.org/10.1137/23m1563967","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 624-641, August 2025. <br/> Abstract.We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with basic knowledge of dynamical systems and numerical methods for ordinary differential equations, we explore a model from mathematical biology where numerical methods fail badly due to catastrophic floating point errors. We analyze the reasons for this behavior by studying the steady states of the model and use the theory of invariants to develop an alternative model suited for numerical simulations. Our story is intended to motivate the combining of analytical knowledge and numerical knowledge, even in those cases where the world looks fine at first sight. We have set up an online repository containing an interactive notebook with all the numerical experiments in this article to make this study fully reproducible and useful for classroom teaching.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"11 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792657","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:; Dissipative Lattice Dynamical Systems 书评:;耗散晶格动力系统
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/24m1675606
Ábel Garab
{"title":"Book Review:; Dissipative Lattice Dynamical Systems","authors":"Ábel Garab","doi":"10.1137/24m1675606","DOIUrl":"https://doi.org/10.1137/24m1675606","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 655-656, August 2025. <br/> Lattice dynamical systems (LDS) are infinite-dimensional systems of ordinary differential equations (ODEs). They can be formulated as ODEs on a Banach space of bi-infinite sequences. They may arise in various ways: some are obtained as discretizations of partial differential equations or integral equations, and others are infinite-dimensional counterparts of finite-dimensional ODE models such as the Hopfield neural network model. This book studies various kinds of LDS that might be of autonomous, nonautonomous, or random nature. It focuses on first showing that the underlying LDS induces an autonomous, nonautonomous, or random semidynamical system, then providing sufficient criteria for the existence of a global, pullback, or random attractor.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"69 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792661","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
SIGEST 团体
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/25m1741492
The Editors
{"title":"SIGEST","authors":"The Editors","doi":"10.1137/25m1741492","DOIUrl":"https://doi.org/10.1137/25m1741492","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 577-577, August 2025. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"3 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792667","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:; Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation 评论:;让民主算数：数学如何改善投票、选举地图和代表性
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/24m1675655
Beth Malmskog
{"title":"Featured Review:; Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation","authors":"Beth Malmskog","doi":"10.1137/24m1675655","DOIUrl":"https://doi.org/10.1137/24m1675655","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 645-650, August 2025. <br/> Democracy: What’s math got to do with it? If you were to ask someone who has not previously studied this topic, you’d likely receive the obvious and simple answer: We count votes, and whoever gets the most votes wins. Okay. If you find someone who follows politics, you might get another answer: We need statistics to take good polls and make predictions. A little more satisfying, and true, but you could say that this type of analysis is more commentary on who is winning and losing in the political process rather than an analysis of the process itself. In the recent book Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation, Ismar Volić gives another answer: Math has everything to do with democracy.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"32 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792664","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
Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians 生成式人工智能的扩散模型：应用数学导论
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/23m1626232
Catherine Higham, Desmond J. Higham, Peter Grindrod
{"title":"Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians","authors":"Catherine Higham, Desmond J. Higham, Peter Grindrod","doi":"10.1137/23m1626232","DOIUrl":"https://doi.org/10.1137/23m1626232","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 607-623, August 2025. <br/> Abstract.Generative artificial intelligence (GAI) refers to algorithms that create synthetic but realistic output. Diffusion models currently offer state-of-the-art performance in GAI for images. They also form a key component in more general tools, including text-to-image generators and large language models. Diffusion models work by adding noise to the available training data and then learning how to reverse the process. The reverse operation may then be applied to new random data in order to produce new outputs. We provide a brief introduction to diffusion models for applied mathematicians and statisticians. Our key aims are to (a) present illustrative computational examples, (b) give a careful derivation of the underlying mathematical formulas involved, and (c) draw a connection with partial differential equation (PDE) diffusion models. We provide code for the computational experiments. We hope that this topic will be of interest to advanced undergraduate and postgraduate students. Portions of the material may also provide useful motivational examples for those who teach courses in stochastic processes, inference, machine learning, PDEs, or scientific computing.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"115 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792656","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
Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint 层次贝叶斯反问题：高维统计观点
IF 10.2 1区 数学
SIAM Review Pub Date : 2025-08-07 DOI: 10.1137/24m1629328
Daniel Sanz-Alonso, Nathan Waniorek
{"title":"Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint","authors":"Daniel Sanz-Alonso, Nathan Waniorek","doi":"10.1137/24m1629328","DOIUrl":"https://doi.org/10.1137/24m1629328","url":null,"abstract":"SIAM Review, Volume 67, Issue 3, Page 543-575, August 2025. <br/> Abstract.This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain nonasymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"27 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144792658","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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