Add the Two-Dimensional Non-Polynomial Function from Lim et al. (2002)

[damar-wicaksono]

The two-dimensional non-polynomial function from Lim et al. (2002)¹ was used in the context of metamodeling exercise (specifically, Gaussian process approach) and is defined as follows:

$$ \mathcal{M}(\boldsymbol{x}) = \frac{1}{6} \left[ \left( 30 + 5 x_1 \sin{\left(5 x_1 \right)} \right) \left( 4 + \exp{\left(-5 x_2 \right)} \right) - 100 \right], $$

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 function, albeit a non-polynomial, exhibits similar behavior to the corresponding polynomial variant.

Footnotes

1. 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. ↩