### Abstract

A general set of quantitative model assessment and analysis tools, termed high-dimensional model representations (HDMR), has been introduced recently for improving the efficiency of deducing highdimensional input-output system behavior. HDMR is 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. To reduce the sampling effort, different analytical basis functions, such as orthonormal polynomials, cubic B splines, and polynomials may be employed to approximate the RS-HDMR component functions. Only one set of random input-output samples is necessary to determine all the RS-HDMR component functions, and a few hundred samples may give a satisfactory approximation, regardless of the dimension of the input variable space. It is shown in an example that judicious use of orthonormal polynomials can provide a sampling saving of ∼10
^{3}
in representing a system compared to employing a direct sampling technique. This paper discusses these practical approaches: their formulas and accuracy along with an illustration from atmospheric modeling.

Original language | English (US) |
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Pages (from-to) | 8721-8733 |

Number of pages | 13 |

Journal | Journal of Physical Chemistry A |

Volume | 106 |

Issue number | 37 |

DOIs | |

State | Published - Sep 19 2002 |

### All Science Journal Classification (ASJC) codes

- Physical and Theoretical Chemistry

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## Cite this

*Journal of Physical Chemistry A*,

*106*(37), 8721-8733. https://doi.org/10.1021/jp014567t