High dimensional model representation for piece‐wise continuous function approximation

R. Chowdhury, B. N. Rao, A. M. Prasad
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引用次数: 54

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.
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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
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