GAMM Mitteilungen最新文献_第8页

A perspective on machine learning methods in turbulence modeling 湍流建模中机器学习方法的展望

GAMM Mitteilungen Pub Date : 2021-03-04 DOI: 10.1002/gamm.202100002

Andrea Beck, Marius Kurz

引用次数: 51

Machine learning for material characterization with an application for predicting mechanical properties 材料表征的机器学习及其预测机械性能的应用

GAMM Mitteilungen Pub Date : 2021-03-04 DOI: 10.1002/gamm.202100003

Anke Stoll, Peter Benner

{"title":"Machine learning for material characterization with an application for predicting mechanical properties","authors":"Anke Stoll, Peter Benner","doi":"10.1002/gamm.202100003","DOIUrl":"10.1002/gamm.202100003","url":null,"abstract":"Currently, the growth of material data from experiments and simulations is expanding beyond processable amounts. This makes the development of new data-driven methods for the discovery of patterns among multiple lengthscales and time-scales and structure-property relationships essential. These data-driven approaches show enormous promise within materials science. The following review covers machine learning (ML) applications for metallic material characterization. Many parameters associated with the processing and the structure of materials affect the properties and the performance of manufactured components. Thus, this study is an attempt to investigate the usefulness of ML methods for material property prediction. Material characteristics such as strength, toughness, hardness, brittleness, or ductility are relevant to categorize a material or component according to their quality. In industry, material tests like tensile tests, compression tests, or creep tests are often time consuming and expensive to perform. Therefore, the application of ML approaches is considered helpful for an easier generation of material property information. This study also gives an application of ML methods on small punch test (SPT) data for the determination of the property ultimate tensile strength for various materials. A strong correlation between SPT data and tensile test data was found which ultimately allows to replace more costly tests by simple and fast tests in combination with ML.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74302427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 28

Topical Issue Applied and Numerical Linear Algebra (2/2) 应用与数值线性代数(2/2)

GAMM Mitteilungen Pub Date : 2020-11-03 DOI: 10.1002/gamm.202000021

Stefan Güttel, Jörg Liesen

引用次数: 3

Preconditioners for Krylov subspace methods: An overview Krylov子空间方法的前置条件:概述

GAMM Mitteilungen Pub Date : 2020-10-21 DOI: 10.1002/gamm.202000015

John W. Pearson, Jennifer Pestana

引用次数: 22

Iterative and doubling algorithms for Riccati-type matrix equations: A comparative introduction riccti型矩阵方程的迭代和加倍算法:比较介绍

GAMM Mitteilungen Pub Date : 2020-10-08 DOI: 10.1002/gamm.202000018

Federico Poloni

{"title":"Iterative and doubling algorithms for Riccati-type matrix equations: A comparative introduction","authors":"Federico Poloni","doi":"10.1002/gamm.202000018","DOIUrl":"10.1002/gamm.202000018","url":null,"abstract":"We review a family of algorithms for Lyapunov- and Riccati-type equations which are all related to each other by the idea of doubling: they construct the iterate <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> of another naturally-arising fixed-point iteration (Xh) via a sort of repeated squaring. The equations we consider are Stein equations X − A∗ X A = Q, Lyapunov equations A∗ X + X A + Q = 0, discrete-time algebraic Riccati equations X = Q + A∗ X(I + G X)−1A, continuous-time algebraic Riccati equations Q + A∗ X + X A − X G X = 0, palindromic quadratic matrix equations A + Q Y + A∗Y2 = 0, and nonlinear matrix equations X + A∗ X−1A = Q. We draw comparisons among these algorithms, highlight the connections between them and to other algorithms such as subspace iteration, and discuss open issues in their theory.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88337416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches 反问题的Krylov方法:考察经典，并引入新的算法方法

GAMM Mitteilungen Pub Date : 2020-09-28 DOI: 10.1002/gamm.202000017

Silvia Gazzola, Malena Sabaté Landman

{"title":"Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches","authors":"Silvia Gazzola, Malena Sabaté Landman","doi":"10.1002/gamm.202000017","DOIUrl":"10.1002/gamm.202000017","url":null,"abstract":"Large-scale linear systems coming from suitable discretizations of linear inverse problems are challenging to solve. Indeed, since they are inherently ill-posed, appropriate regularization should be applied; since they are large-scale, well-established direct regularization methods (such as Tikhonov regularization) cannot often be straightforwardly employed, and iterative linear solvers should be exploited. Moreover, every regularization method crucially depends on the choice of one or more regularization parameters, which should be suitably tuned. The aim of this paper is twofold: (a) survey some well-established regularizing projection methods based on Krylov subspace methods (with a particular emphasis on methods based on the Golub-Kahan bidiagonalization algorithm), and the so-called hybrid approaches (which combine Tikhonov regularization and projection onto Krylov subspaces of increasing dimension); (b) introduce a new principled and adaptive algorithmic approach for regularization similar to specific instances of hybrid methods. In particular, the new strategy provides reliable parameter choice rules by leveraging the framework of bilevel optimization, and the links between Gauss quadrature and Golub-Kahan bidiagonalization. Numerical tests modeling inverse problems in imaging illustrate the performance of existing regularizing Krylov methods, and validate the new algorithms.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76182732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

A survey of subspace recycling iterative methods 子空间循环迭代方法综述

GAMM Mitteilungen Pub Date : 2020-09-20 DOI: 10.1002/gamm.202000016

Kirk M. Soodhalter, Eric de Sturler, Misha E. Kilmer

{"title":"A survey of subspace recycling iterative methods","authors":"Kirk M. Soodhalter, Eric de Sturler, Misha E. Kilmer","doi":"10.1002/gamm.202000016","DOIUrl":"10.1002/gamm.202000016","url":null,"abstract":"This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial vectors over a sequence of linear systems with slowly changing coefficient matrices, multiple right-hand sides, or both. The subspace information that is recycled is usually generated during the run of an iterative method (usually a Krylov subspace method) on one or more of the systems. Following introduction of definitions and notation, we examine the history of early augmentation schemes along with deflation preconditioning schemes and their influence on the development of recycling methods. We then discuss a general residual constraint framework through which many augmented Krylov and recycling methods can both be viewed. We review several augmented and recycling methods within this framework. We then discuss some known effective strategies for choosing subspaces to recycle before taking the reader through more recent developments that have generalized recycling for (sequences of) shifted linear systems, some of them with multiple right-hand sides in mind. We round out our survey with a brief review of application areas that have seen benefit from subspace recycling methods.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76431675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 31

Limited-memory polynomial methods for large-scale matrix functions 大规模矩阵函数的有限记忆多项式方法

GAMM Mitteilungen Pub Date : 2020-09-10 DOI: 10.1002/gamm.202000019

Stefan Güttel, Daniel Kressner, Kathryn Lund

引用次数: 11

A literature survey of matrix methods for data science 数据科学中矩阵方法的文献综述

GAMM Mitteilungen Pub Date : 2020-09-10 DOI: 10.1002/gamm.202000013

Martin Stoll

引用次数: 17

Topical Issue Applied and Numerical Linear Algebra (1/2) 应用与数值线性代数(1/2)

GAMM Mitteilungen Pub Date : 2020-09-10 DOI: 10.1002/gamm.202000020

Stefan Güttel, Jörg Liesen

引用次数: 0