{"title":"High dimensional model representation for piece‐wise continuous function approximation","authors":"R. Chowdhury, B. N. Rao, A. M. Prasad","doi":"10.1002/CNM.1053","DOIUrl":null,"url":null,"abstract":"High dimensional model representation (HDMR) approximates multivariate functions in such a way that the component functions of the approximation are ordered starting from a constant and gradually approaching to multivariance as we proceed along the terms like first-order, second-order and so on. Until now HDMR applications include construction of a computational model directly from laboratory/field data, creating an efficient fully equivalent operational model to replace an existing time-consuming mathematical model, identification of key model variables, global uncertainty assessments, efficient quantitative risk assessments, etc. In this paper, the potential of HDMR for tackling univariate and multivariate piece-wise continuous functions is explored. Eight numerical examples are presented to illustrate the performance of HDMR for approximating a univariate or a multivariate piece-wise continuous function with an equivalent continuous function. Copyright © 2007 John Wiley & Sons, Ltd.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"24 1","pages":"1587-1609"},"PeriodicalIF":0.0000,"publicationDate":"2007-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1053","citationCount":"54","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Numerical Methods in Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/CNM.1053","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 54
分段连续函数近似的高维模型表示
高维模型表示(HDMR)以这样一种方式逼近多元函数,即近似值的分量函数从常数开始排序,随着我们继续进行一阶,二阶等项,逐渐接近多方差。到目前为止,HDMR的应用包括直接从实验室/现场数据构建计算模型,创建高效的全等效操作模型以取代现有耗时的数学模型,识别关键模型变量,全局不确定性评估,高效的定量风险评估等。本文探讨了HDMR在处理单变量和多变量分段连续函数方面的潜力。给出了八个数值例子来说明HDMR用等价连续函数逼近单变量或多变量分段连续函数的性能。版权所有©2007 John Wiley & Sons, Ltd
本文章由计算机程序翻译,如有差异,请以英文原文为准。