Efficient input-output model representations

A family of multivariate representations is presented to capture the input- output relationships of physical systems with many input variables. The hig h-dimensional model representations (HDMR) are based on the ansatz that for most physical systems, only relatively low order correlations of the input variables will have an impact on the output. Application of the HDMR tools can dramatically reduce the computational effort in representing the input -output relationships of a physical system. Two types of HDMR's are present ed in this paper: ANOVA-HDMR is the same as the analysis of variance (ANOVA ) decomposition used in statistics. Another cut-HDMR will be shown to be co mputationally more efficient than the ANOVA decomposition. Three test examp les are given to illustrate the high computational efficiency of cut-HDMR. (C) 1999 Elsevier Science B.V.