Virtual Library of Simulation Experiments:

Calibration/Tuning Test Problems

Functional Data Test Problems

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Environmental Model Function

Description:

Input dimensions: 4

Output dimensions: d_Y = d_s x d_t

The Environmental Model function models a pollutant spill caused by a chemical accident. C(x) is the concentration of the pollutant at the space-time vector (s, t), where 0 ≤ s ≤ 3 and t > 0. I is the indicator function.

A mass M of the pollutant is spilled at each of two locations, denoted by the space-time vectors (0, 0) and
(L, τ). Each element of the response is a scaled concentration of the pollutant at the space-time vector
(s_i, t_j), for i = 1, …, d_s and j = 1, …, d_t.

Bliznyuk et al. (2008) use d_s = 5 locations and d_t = 200 times: s = 0, 0.5, 1, 1.5, 2.5 and t = 0.3, 0.6, …, 50.7, 60.

In the plot above, the response is shown as a function of s and t, for the values M = 10, D = 0.07, L = 1.505 and τ = 30.1525.

Input Domain:

The input parameters of interest and their usual input ranges are:

M ∈ [7, 13]	mass of pollutant spilled at each location
D ∈ [0.02, 0.12]	diffusion rate in the channel
L ∈ [0.01, 3]	location of the second spill
τ ∈ [30.01, 30.295]	time of the second spill

Code:

Reference:

Bliznyuk, N., Ruppert, D., Shoemaker, C., Regis, R., Wild, S., & Mugunthan, P. (2008). Bayesian calibration and uncertainty analysis for computationally expensive models using optimization and radial basis function approximation. Journal of Computational and Graphical Statistics, 17(2).

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For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.