The one-dimensional sine function from Currin et al. (1988)[^Currin] was used as a test function for Gaussian process metamodeling exercise and it is defined as follows:
where $x$ is a uniform random variable in $[0, 1]$.
[^Currin]: C. Currin, T. Mitchell, M. Morris, and D. Ylvisaker, “A Bayesian Approach to the Design and Analysis of Computer Experiments,” ORNL-6498, 814584, Jan. 1988. doi: 10.2172/814584.
The one-dimensional sine function from Currin et al. (1988)[^Currin] was used as a test function for Gaussian process metamodeling exercise and it is defined as follows:
$$ \mathcal{M}(x) = \sin{\left( 2 \pi (x - 0.1) \right)}, $$
where $x$ is a uniform random variable in $[0, 1]$.
[^Currin]: C. Currin, T. Mitchell, M. Morris, and D. Ylvisaker, “A Bayesian Approach to the Design and Analysis of Computer Experiments,” ORNL-6498, 814584, Jan. 1988. doi: 10.2172/814584.