Global uncertainty assessments by high dimensional model representations (HDMR)

Genyuan Li, Sheng Wei Wang, Herschel Albert Rabitz, Sookyun Wang, Peter R. Jaffe

Research output: Contribution to journalArticlepeer-review

173 Scopus citations


A general set of quantitative model assessment and analysis tools, termed high-dimensional model representations (HDMR), have been introduced recently for high dimensional input-output systems. HDMR are a particular family of representations where each term in the representation reflects the independent and cooperative contributions of the inputs upon the output. When data are randomly sampled, a RS(random sampling)-HDMR can be constructed, which is an efficient tool to provide a fully global statistical analysis of a model. The individual RS-HDMR component functions have a direct statistical correlation interpretation. This relation permits the model output variance σ2 to be decomposed into its input contributions σ2 = Σiσ2i + Σi<j σ2ij +. due to the independent variable action σ2i, the pair correlation action σ2ij, etc. The information gained from this decomposition can be valuable for attaining a physical understanding of the origins of output uncertainty as well as suggesting additional laboratory/field studies or model refinements to best improve the quality of the model. To reduce sampling effort, the RS-HDMR component functions are approximately represented by orthonormal polynomials. Only one randomly sampled set of input-output data is needed to determine all σi, σij, etc. and a few hundred samples may give reliable results. This paper presents its methodology and applications on an atmospheric photochemistry model and a trace metal bioremediation model.

Original languageEnglish (US)
Pages (from-to)4445-4460
Number of pages16
JournalChemical Engineering Science
Issue number21
StatePublished - Nov 4 2002

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • General Chemical Engineering
  • Industrial and Manufacturing Engineering


  • Global uncertainty analysis
  • High dimensional model representation
  • Monte Carlo method


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