Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] aeei_v1_0.tar.gz(320 Kbytes)|
|Manuscript Title: Fitting sparse multidimensional data with low-dimensional terms|
|Authors: Sergei Manzhos, Koichi Yamashita, Tucker Carrington Jr.|
|Program title: RS_HDMR_NN|
|Catalogue identifier: AEEI_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 180(2009)2002|
|Programming language: MatLab R2007b.|
|Computer: any computer running MatLab.|
|Operating system: Windows XP, Windows Vista, UNIX, Linux.|
|Keywords: neural networks, high dimensional model representation, functional approximation, fitting and interpolation.|
|PACS: 31.50.Bc, 31.50.Df.|
External routines: Neural Network Toolbox Version 5.1 (R2007b).
Nature of problem:
Fitting a smooth, easily integratable and differentiatable, function to a very sparse (~2-3 points per dimension) multidimensional (D ≥ 6) large (~104-105 data) dataset.
A multivariate function is represented as a sum of a small number of terms each of which is a low-dimensional function of optimised coordinates. The optimal coordinates reduce both the dimensionality and the number of the terms. Neural networks (including exponential neurons) are used to obtain a general and robust method and a functional form which is easily differentiated and integrated (in the case of exponential neurons).
Depends strongly on the dataset to be modelled and the chosen structure of the approximating function, ranges from about a minute for ~103 data in 3-D to about a day for ~105 data in 15-D.
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