The 20-dimensional function was used in a metamodeling exercise[^1]; it features a sparse polynomial structure in high-dimension but with low degree of interaction. The function reads:
[^1]: N. Alemazkoor and H. Meidani, “A near-optimal sampling strategy for sparse recovery of polynomial chaos expansions,” Journal of Computational Physics, vol. 371, pp. 137–151, Oct. 2018, doi: 10.1016/j.jcp.2018.05.025.
The 20-dimensional function was used in a metamodeling exercise[^1]; it features a sparse polynomial structure in high-dimension but with low degree of interaction. The function reads:
$$ \mathcal{M}(\boldsymbol{x}) = \sum_{m = 1}^{19} xm x{m + 1}, $$
where $X_i \sim \mathcal{U}(-1, 1)$.
[^1]: N. Alemazkoor and H. Meidani, “A near-optimal sampling strategy for sparse recovery of polynomial chaos expansions,” Journal of Computational Physics, vol. 371, pp. 137–151, Oct. 2018, doi: 10.1016/j.jcp.2018.05.025.