Multicut-HDMR with an application to an ionospheric model

Genyuan Li, Jacqueline Schoendorf, Tak San Ho, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


A new High Dimensional Model Representation (HDMR) tool, Multicut-HDMR, is introduced and applied to an ionospheric electron density model. HDMR is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high-dimensional input-output system behavior. HDMR describes an output [f(x)] in terms of its input variables (x = {x 1, x 2, . . . ., x n}) via a series of finite, hierarchical, correlated function expansions. Various forms of HDMR are constructed for different purposes such as modeling laboratory or field data, or reproducing a complicated mathematical model. The Cut-HDMR technique, which expresses f(x) with respect to a specified reference point x̄ in the input space, is appropriate when the input space is sampled in an orderly fashion. However, if the desired domain of the input space is too large, the HDMR function expansion may not converge, and Cut-HDMR will be unable to accurately approximate f(x). The new Multicut-HDMR technique addresses this problem through the use of multiple reference points in the input space.

Original languageEnglish (US)
Pages (from-to)1149-1156
Number of pages8
JournalJournal of Computational Chemistry
Issue number9
StatePublished - Jul 15 2004

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • Computational Mathematics


  • HDMR
  • Ionospheric electron density


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