Add the three-dimension test function with Asymptotes from Dette and Pepelyshev (2010)

[damar-wicaksono]

The three-dimensional function from Dette and Pepelyshev (2010)¹ is a test function used in the context of metamodeling (specifically, design of computer experiments to construct metamodels). The function reads as follows:

$$ \mathcal{M}(\boldsymbol{x}) = 100 \left( \exp{\left({\frac{-2}{x_1^{1.75}}}\right)} + \exp{\left({\frac{-2}{x_2^{1.5}}}\right)} + \exp{\left({\frac{-2}{x_3^{1.25}}}\right)} \right) $$

where $\boldsymbol{x} = \{ x_1, x_2, x_3 \}$ is the vector of input variables modeled as an independent uniform random variable in $[0, 1]^3$. The function features asymptotes at the left boundaries of the design space.

Footnotes

1. H. Dette and A. Pepelyshev, "Generalized latin hypercube design for computer experiments," Technometrics, vol. 52, no. 4, pp. 421-429, 2010. doi: 10.1198/TECH.2010.09157. See Eq. (4), Section 3.1. ↩