While the use of high-fidelity simulation models such as finite element or computational fluid dynamics models for optimization of engineering design problems has become very common, the computational expense of performing numerous runs of such models remains for most part an unsolved issue. One approach to reduce the computational expense is to approximate the simulation model by a less expensive meta-model.
A typical approximation technique consists of two phases:
1. Design of experiments (DOE), in which a sample of experiments in the design space is selected.
2. Meta-modeling, in which the response values from the DOE are evaluated and used to build a reasonably accurate approximation for response function.
The existing DOE methods can be classified into two major groups: the first class of techniques, often referred to as classical DOE, accounts for inherent randomness in the behavior of a model and is mostly appropriate for physical experimentation with inherent measurement errors. The second class of techniques, often referred to as space filling, is especially appropriate for deterministic computer simulations. Examples of this second class of techniques include Latin Hypercube, Orthogonal array, maximum entropy etc. Among meta-modeling techniques, interpolative approaches such as Bayesian meta-modeling widely use space filling DOE.