The two-dimensional polynomial function from Lim et al. (2002)[^Lim] was used in the context of metamodeling exercise (specifically, Gaussian process approach) and is defined as follows:
where $\boldsymbol{x} = { x_1, x_2 }$ is the vector of input variables modeled as an independent uniform random vector in $[0, 1]^2$. The test function is a polynomial function of degree 5 (and therefore, smooth albeit complex).
[^Lim]: Y. B. Lim, J. Sacks, W. J. Studden, and W. J. Welch, “Design and analysis of computer experiments when the output is highly correlated over the input space,” Canadian Journal of Statistics, vol. 30, no. 1, pp. 109–126, 2002, doi: 10.2307/3315868.
The two-dimensional polynomial function from Lim et al. (2002)[^Lim] was used in the context of metamodeling exercise (specifically, Gaussian process approach) and is defined as follows:
$$ \mathcal{M}(\boldsymbol{x}) = 9 + \frac{5}{2} x_1 - \frac{35}{2} x_2 + \frac{5}{2} x_1 x_2 + 19 x_2^2 - \frac{15}{2} x_1^3 - \frac{5}{2} x_1 x_2^2 - \frac{11}{2} x_2^4 + x_1^3 x_2^2, $$
where $\boldsymbol{x} = { x_1, x_2 }$ is the vector of input variables modeled as an independent uniform random vector in $[0, 1]^2$. The test function is a polynomial function of degree 5 (and therefore, smooth albeit complex).
[^Lim]: Y. B. Lim, J. Sacks, W. J. Studden, and W. J. Welch, “Design and analysis of computer experiments when the output is highly correlated over the input space,” Canadian Journal of Statistics, vol. 30, no. 1, pp. 109–126, 2002, doi: 10.2307/3315868.