通过多项式混沌扩展张量计算统计矩

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-04-15 DOI:10.1137/23m155428x

Rafael Ballester-Ripoll

{"title":"通过多项式混沌扩展张量计算统计矩","authors":"Rafael Ballester-Ripoll","doi":"10.1137/23m155428x","DOIUrl":null,"url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 289-308, June 2024. <br/> Abstract. We present an algorithm for estimating higher-order statistical moments of multidimensional functions expressed as polynomial chaos expansions (PCE). The algorithm starts by decomposing the PCE into a low-rank tensor network using a combination of tensor-train and Tucker decompositions. It then efficiently calculates the desired moments in the compressed tensor domain, leveraging the highly linear structure of the network. Using three benchmark engineering functions, we demonstrate that our approach offers substantial speed improvements over alternative algorithms while maintaining a minimal and adjustable approximation error. Additionally, our method can calculate moments even when the input variable distribution is altered, incurring only a small additional computational cost and without requiring retraining of the regressor.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":"99 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions\",\"authors\":\"Rafael Ballester-Ripoll\",\"doi\":\"10.1137/23m155428x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 289-308, June 2024. <br/> Abstract. We present an algorithm for estimating higher-order statistical moments of multidimensional functions expressed as polynomial chaos expansions (PCE). The algorithm starts by decomposing the PCE into a low-rank tensor network using a combination of tensor-train and Tucker decompositions. It then efficiently calculates the desired moments in the compressed tensor domain, leveraging the highly linear structure of the network. Using three benchmark engineering functions, we demonstrate that our approach offers substantial speed improvements over alternative algorithms while maintaining a minimal and adjustable approximation error. Additionally, our method can calculate moments even when the input variable distribution is altered, incurring only a small additional computational cost and without requiring retraining of the regressor.\",\"PeriodicalId\":56064,\"journal\":{\"name\":\"Siam-Asa Journal on Uncertainty Quantification\",\"volume\":\"99 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siam-Asa Journal on Uncertainty Quantification\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1137/23m155428x\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siam-Asa Journal on Uncertainty Quantification","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1137/23m155428x","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

SIAM/ASA 不确定性量化期刊》第 12 卷第 2 期第 289-308 页，2024 年 6 月。摘要。我们提出了一种估计以多项式混沌展开（PCE）表示的多维函数的高阶统计矩的算法。该算法首先使用张量-训练和塔克分解相结合的方法，将 PCE 分解为低秩张量网络。然后，该算法利用网络的高度线性结构，在压缩张量域中高效计算所需的矩。我们利用三个基准工程函数证明，与其他算法相比，我们的方法大大提高了速度，同时保持了最小的可调节近似误差。此外，即使输入变量的分布发生变化，我们的方法也能计算矩，只需少量额外计算成本，且无需重新训练回归器。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Computing Statistical Moments Via Tensorization of Polynomial Chaos Expansions

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 289-308, June 2024.
Abstract. We present an algorithm for estimating higher-order statistical moments of multidimensional functions expressed as polynomial chaos expansions (PCE). The algorithm starts by decomposing the PCE into a low-rank tensor network using a combination of tensor-train and Tucker decompositions. It then efficiently calculates the desired moments in the compressed tensor domain, leveraging the highly linear structure of the network. Using three benchmark engineering functions, we demonstrate that our approach offers substantial speed improvements over alternative algorithms while maintaining a minimal and adjustable approximation error. Additionally, our method can calculate moments even when the input variable distribution is altered, incurring only a small additional computational cost and without requiring retraining of the regressor.

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

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.