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