High-dimensional model representation

High-dimensional model representation is a finite expansion for a given multivariable function. The expansion is first described by Sobol as

$f(\mathbf{x}) = f_0+ \sum_{i=1}^nf_i(x_i)+ \sum_{i,j=1 \atop i<j}^n f_{ij}(x_{j},x_{j})+ \cdots + f_{12\ldots n}(x_1,\ldots,x_n).$

The method, used to determine the right hand side functions, is given in Sobol's paper.^[1] A review can be found here: High Dimensional Model Representation (HDMR): Concepts and Applications.

See also

• Volterra series

References

1. Sobol', I. M. (1993), "Sensitivity estimates for nonlinear mathematical models", Mathematical Modeling and Computational Experiment 1 (4): 407–414 (1995), MR 1335161.