### Abstract

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 language | English (US) |
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Pages (from-to) | 1149-1156 |

Number of pages | 8 |

Journal | Journal of Computational Chemistry |

Volume | 25 |

Issue number | 9 |

DOIs | |

State | Published - Jul 15 2004 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Computational Mathematics

### Keywords

- HDMR
- Ionospheric electron density

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## Cite this

*Journal of Computational Chemistry*,

*25*(9), 1149-1156. https://doi.org/10.1002/jcc.20040