Test Functions for Metamodeling

The table below listed the available test functions typically used in the comparison of metamodeling approaches.

Name	Spatial Dimension	Constructor
Ackley	M	Ackley()
Alemazkoor & Meidani (2018) 2D	2	Alemazkoor2D()
Alemazkoor & Meidani (2018) 20D	20	Alemazkoor20D()
Borehole	8	Borehole()
Damped Cosine	1	DampedCosine()
Damped Oscillator	7	DampedOscillator()
Flood	8	Flood()
Forrester et al. (2008)	1	Forrester2008()
(1st) Franke	2	Franke1()
(2nd) Franke	2	Franke2()
(3rd) Franke	2	Franke3()
(4th) Franke	2	Franke4()
(5th) Franke	2	Franke5()
(6th) Franke	2	Franke6()
Gramacy (2007) 1D Sine	1	Gramacy1DSine()
McLain S1	2	McLainS1()
McLain S2	2	McLainS2()
McLain S3	2	McLainS3()
McLain S4	2	McLainS4()
McLain S5	2	McLainS5()
Oakley & O’Hagan (2002) 1D	1	Oakley1D()
OTL Circuit	6 / 20	OTLCircuit()
Piston Simulation	7 / 20	Piston()
Webster et al. (1996) 2D	2	Webster2D()
Sulfur	9	Sulfur()
Welch1992	20	Welch1992()
Wing Weight	10	WingWeight()

In a Python terminal, you can list all the available functions relevant for metamodeling applications using list_functions() and filter the results using the tag parameter:

import uqtestfuns as uqtf

uqtf.list_functions(tag="metamodeling")

 No.      Constructor       Dimension   Description
-----  ------------------  -----------  ----------------------------------------------------------------------------
  1         Ackley()            M       Optimization test function from Ackley (1987)
  2     Alemazkoor20D()        20       High-dimensional low-degree polynomial from Alemazkoor & Meidani (2018)
  3      Alemazkoor2D()         2       Low-dimensional high-degree polynomial from Alemazkoor & Meidani (2018)
  4        Borehole()           8       Borehole function from Harper and Gupta (1983)
  5      DampedCosine()         1       One-dimensional damped cosine from Santner et al. (2018)
  6    DampedOscillator()       8       Damped oscillator model from Igusa and Der Kiureghian (1985)
  7         Flood()             8       Flood model from Iooss and Lemaître (2015)
  8     Forrester2008()         1       One-dimensional function from Forrester et al. (2008)
  9        Franke1()            2       (1st) Franke function from Franke (1979)
 10        Franke2()            2       (2nd) Franke function from Franke (1979)
 11        Franke3()            2       (3rd) Franke function from Franke (1979)
 12        Franke4()            2       (4th) Franke function from Franke (1979)
 13        Franke5()            2       (5th) Franke function from Franke (1979)
 14        Franke6()            2       (6th) Franke function from Franke (1979)
 15     Gramacy1DSine()         1       One-dimensional sine function from Gramacy (2007)
 16        McLainS1()           2       McLain S1 function from McLain (1974)
 17        McLainS2()           2       McLain S2 function from McLain (1974)
 18        McLainS3()           2       McLain S3 function from McLain (1974)
 19        McLainS4()           2       McLain S4 function from McLain (1974)
 20        McLainS5()           2       McLain S5 function from McLain (1974)
 21       OTLCircuit()          6       Output transformerless (OTL) circuit model from Ben-Ari and Steinberg (2007)
 22        Oakley1D()           1       One-dimensional function from Oakley and O'Hagan (2002)
 23         Piston()            7       Piston simulation model from Ben-Ari and Steinberg (2007)
 24         Sulfur()            9       Sulfur model from Charlson et al. (1992)
 25       Webster2D()           2       2D polynomial function from Webster et al. (1996).
 26       Welch1992()          20       20-Dimensional function from Welch et al. (1992)
 27       WingWeight()         10       Wing weight model from Forrester et al. (2008)