12/19/2023 0 Comments Latin hypercube designFinal thoughts are given on opportunities for future research. The discussion starts with the early developments in optimization of the point selection and goes all the way to the pitfalls of the indiscriminate use of Latin hypercube designs. Any of the two-dimensional projections is still a Latin hypercube design with the same p15 points (although, for this particular case, the x 1 x 2 projection is the best in terms of space lling). The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n non-attacking rooks on an n x n chessboard such. The levels are spaced evenly from the lower bound to the upper bound of the factor. This results a scheme where each recipe is tested once in each furnace. In a Latin Hypercube, each factor has as many levels as there are runs in the design. Here the values (A, B and C) correspond to the three diffusion recipes and the parameter (p1 to p3) corresponds to three furnaces. Figure 3(a) illustrates the case of a Latin hypercube design with d3 dimensions and p15 points. 3.1.11 Latin Hypercube Design Table 3.3 shows a Latin Hypercube design with three parameters. This paper provides a tutorial on Latin hypercube design of experiments, highlighting potential reasons of its widespread use. Latin hypercube samples are non-collapsing. The Latin hypercube structure allows one to achieve both the space-filling. Among the strategies devised for computer experiments, Latin hypercube designs have become particularly popular. Latin hypercube designs (LHD) play an important role in computer experiments. LHS is based on the Latin square design, which has a single sample in each row and column. It is widely used in Monte Carlo simulation, because it can drastically reduce the number of runs necessary to achieve a reasonably accurate result. The first step for a successful surrogate modeling and statistical analysis is the planning of the input configuration that is used to exercise the simulation code. Latin hypercube sampling is a widely-used method to generate controlled random samples. Latin Hypercube Sampling (LHS) is a way of generating random samples of parameter values. Generally, when simulations are time consuming, a surrogate model replaces the computer code in further studies (e.g., optimization, sensitivity analysis, etc.). The growing power of computers enabled techniques created for design and analysis of simulations to be applied to a large spectrum of problems and to reach high level of acceptance among practitioners.
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