Analysis of computationally demanding models with continuous and categorical inputs

The analysis of many physical and engineering problems involves running complex computational models (e.g., simulation models and computer codes). With problems of this type, it is important to understand the relationships between the input (whose values are often imprecisely known) and the output variables, and to characterize the uncertainty in the output. Often, some of the input variables are categorical in nature (e.g., pointer variables to alternative models or different types of material, etc.). A computational model that sufficiently represents reality is often very costly in terms of run time. When the models are computationally demanding, meta-model approaches to their analysis have been shown to be very useful. However, the most popular meta-models for computational computer models do not explicitly allow for categorical input variables. In this case, categorical inputs are simply ordered in some way and treated as continuous variables in the estimation of a meta-model. In many cases, this can lead to undesirable and misleading results. In this paper, two meta-models based on functional ANOVA decomposition are presented that explicitly allow for an appropriate treatment of categorical inputs. The effectiveness of the presented meta-models in the analysis of models with continuous and categorical inputs is illustrated with several test cases and also with results from a real analysis.