## High Dimensional Model Representation

Global sensitivity analysis is a very important part of the model evaluation process and should be applied in order to assess and increase the reliability of computer models. However, many models used in environmental engineering and other fields have a large number of uncertain parameters and are computationally expensive to run. This restricts the usage of traditional methods of global sensitivity analysis such as Monte Carlo analysis due to the computational expense of the model and the difficulty in interpreting the results (e.g. scatter plots) for large numbers of parameters.

The high dimensional model representation (HDMR) method is an expansion with a hierarchical form in terms of the input parameters and produces a detailed mapping of the input parameter space to selected outputs which is fundamental to global sensitivity analysis. Sensitivity indices are calculated in an automatic way that can then be directly used in importance ranking and to explore parameter interactions. The HDMR expansion can also be used as a metamodel instead of the original model. There are two commonly used HDMR expansions: cut-HDMR and random sampling (RS)-HDMR. The GUI-HDMR software is based on the RS-HDMR approach, where all component functions are approximated by orthonormal polynomials using only one set of random (or quasi-random) samples.

The HDMR method can cope with highly non-linear (and non-monotonic) model responses, parameter interactions and a large input space dimension in a computationally efficient way. An introduction to the RS-HDMR approach can be found in the GUI-HDMR software documentation and the literature stated in there.