Virtual Library of Simulation Experiments:

Test Functions and Datasets

Welch et al. (1992) Function


Dimensions: 20

For input variable screening purposes, it can be found that some input variables of this function have a very high effect on the output, compared to other input variables. As Welch et al. (1992) point out, interactions and nonlinear effects make this function challenging.

Note: Ben-Ari & Steinberg (2008) use -5x1 as the fifth term, instead of -5x19.

Input Domain:

This function is evaluated on: xi ∈ [-0.5, 0.5], for all i = 1, …, 20.



Ben-Ari, E. N., & Steinberg, D. M. (2007). Modeling data from computer experiments: an empirical comparison of kriging with MARS and projection pursuit regression. Quality Engineering, 19(4), 327-338.

Welch, W. J., Buck, R. J., Sacks, J., Wynn, H. P., Mitchell, T. J., & Morris, M. D. (1992). Screening, predicting, and computer experiments. Technometrics, 34(1), 15-25.

For questions or comments, please email Derek Bingham at: