Correlation method for variance reduction of Monte Carlo integration in RS-HDMR

Genyuan Li, Herschel Rabitz, Sheng Wei Wang, Panos G. Georgopoulos

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


The High Dimensional Model Representation (HDMR) technique is a procedure for efficiently representing high-dimensional functions. A practical form of the technique, RS-HDMR, is based on randomly sampling the overall function and utilizing orthonormal polynomial expansions. The determination of expansion coefficients employs Monte Carlo integration, which controls the accuracy of RS-HDMR expansions. In this article, a correlation method is used to reduce the Monte Carlo integration error. The determination of the expansion coefficients becomes an iteration procedure, and the resultant RS-HDMR expansion has much better accuracy than that achieved by direct Monte Carlo integration. For an illustration in four dimensions a few hundred random samples are sufficient to construct an RS-HDMR expansion by the correlation method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples.

Original languageEnglish (US)
Pages (from-to)277-283
Number of pages7
JournalJournal of Computational Chemistry
Issue number3
StatePublished - Feb 2003

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • Computational Mathematics


  • Atmospheric chemistry
  • Correlation method with Monte Carlo integration
  • HDMR
  • High dimensional systems
  • Random sampling


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