Add the Two-Dimensional Test Function from Cheng and Sandu (2010)

[damar-wicaksono]

The two-dimensional non-linear test function from Cheng and Sandu (2010)¹ is defined as follows:

$$ \mathcal{M}(\boldsymbol{x}) = \cos{\left( x_1 + x_2 \right)} \exp{\left( x_1 x_2 \right)}, $$

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 was used as a test function in the context of metamodeling exercise in Cheng and Sandu (2010)¹ (specifically, non-intrusive polynomial chaos approach).

Footnotes

1. H. Cheng and A. Sandu, “Collocation least-squares polynomial chaos method,” in Proceedings of the 2010 Spring Simulation Multiconference, Orlando, Florida: Society for Computer Simulation International, 2010, pp. 1–6. doi: 10.1145/1878537.1878621. ↩ ↩²