Deterministic computer simulations are becoming widely used in science and engineering. Important examples are simulations of characteristics of logistical systems and physical phenomena of products or processes. As one simulation run is often time-consuming, the simulation model is often replaced by an approximating model, based on simulations in some points. We call such a set of simulation points a design. Other names for the approximating model used in the literature are: metamodel, surrogate model, compact model, regression model.
As is recognized by several authors, a design of computer experiments (DoCE) should at least be space-filling in some sense. When no details on the functional behavior of the response parameters are available, it is important to obtain information from the entire design space. Therefore, design points should be 'evenly spread' over the entire region. Several space-filling criteria are discussed in the literature, e.g. maximin, minimax, IMSE, and maximum entropy. On this webpage, we mainly concentrate on maximin designs. A maximin design is a set of points such that the separation distance (i.e. the minimal distance among pairs of points) is maximal.
Another criterion often used is that a DoCE should be non-collapsing. When one of the design parameters has (almost) no influence on the simulation outcome, two design points that differ only in this parameter will 'collapse', i.e. they can be considered as the same point that is simulated twice. For deterministic simulation this is not a desirable situation. Therefore, two design points should not share any coordinate values when it is not known a priori which dimensions are important. For this reason, the design is often restricted to a d-dimensional grid of n levels in every dimension. The design is constructed such that each level occurs only once. Such a design is called a Latin hypercube design (LHD).
For a good survey on Design of Computer Experiments we refer to:
Finding a design scheme for expensive computer experiments is a difficult task. On this website, we provide many of such designs. We mainly concentrate on maximin designs, which are often used in the area of computer simulations.
This website contains a collection of space-filling designs. These designs can be downloaded and used in your specific simulation environment.