High-dimensional model representations generated from low order terms-lp-RS-HDMR

L. I. Genyuan, Maxim Artamonov, Herschel Albert Rabitz, Sheng Wei Wang, Panos G. Georgopoulos, Metin Demiralp

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.

Original languageEnglish (US)
Pages (from-to)647-656
Number of pages10
JournalJournal of Computational Chemistry
Volume24
Issue number5
DOIs
StatePublished - Apr 15 2003

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Computational Mathematics

Keywords

  • Atmospheric modeling
  • HDMR
  • Monte Carlo integration
  • Random sampling

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    Genyuan, L. I., Artamonov, M., Rabitz, H. A., Wang, S. W., Georgopoulos, P. G., & Demiralp, M. (2003). High-dimensional model representations generated from low order terms-lp-RS-HDMR. Journal of Computational Chemistry, 24(5), 647-656. https://doi.org/10.1002/jcc.10232