emukit.test_functions package

Subpackages

• emukit.test_functions.multi_fidelity package
  • Submodules
    • multi_fidelity_borehole_function()
    • multi_fidelity_branin_function()
    • multi_fidelity_currin_function()
    • multi_fidelity_hartmann_3d()
    • multi_fidelity_park_function()
  • Module contents
• emukit.test_functions.quadrature package
  • Submodules
    • univariate_approximate_ground_truth_integral()
    • bivariate_approximate_ground_truth_integral()
    • circular_gaussian()
    • hennig1D()
    • sombrero2D()
  • Module contents
• emukit.test_functions.sensitivity package
  • Submodules
    • Ishigami
      • Ishigami.fidelity1()
      • Ishigami.fidelity2()
      • Ishigami.fidelity3()
      • Ishigami.fidelity4()
      • Ishigami.f0()
      • Ishigami.f1()
      • Ishigami.f2()
      • Ishigami.f3()
      • Ishigami.f12()
      • Ishigami.f13()
      • Ishigami.f23()
      • Ishigami.f123()
  • Module contents

Submodules

emukit.test_functions.branin.branin_function()

Two-dimensional Branin, often used as an optimization benchmark.

Based on: https://www.sfu.ca/~ssurjano/branin.html

\[f(\mathbf{x}) = (x_2 - b x_1 ^ 2 + c x_1 - r) ^ 2 + s(1 - t) \cos(x_1) + s\]

where:

\[ \begin{align}\begin{aligned}b = 5.1 / (4 \pi ^ 2)\\c = 5 /\pi\\r = 6\\s = 10\\t = 1 / (8\pi)\end{aligned}\end{align} \]

emukit.test_functions.forrester.multi_fidelity_forrester_function(high_fidelity_noise_std_deviation=0, low_fidelity_noise_std_deviation=0)

Two-level multi-fidelity forrester function where the high fidelity is given by:

\[f(x) = (6x - 2)^2 \sin(12x - 4)\]

and the low fidelity approximation given by:

\[f_{low}(x) = 0.5 f_{high}(x) + 10 (x - 0.5) + 5\]

Parameters:

• high_fidelity_noise_std_deviation – Standard deviation of observation noise on high fidelity observations. Defaults to zero.

• low_fidelity_noise_std_deviation – Standard deviation of observation noise on low fidelity observations. Defaults to zero.

Returns:

Tuple of user function object and parameter space object

emukit.test_functions.forrester.forrester_function(noise_standard_deviation=0)

Forrester function

\[f(x) = (6x - 2)^2 \sin(12x - 4)\]

Parameters:

noise_standard_deviation – Standard deviation of normally distributed observation noise

Returns:

Tuple of function and parameter space object

emukit.test_functions.forrester.forrester(x, sd=0)

Forrester function

Parameters:

• x – input vector to be evaluated

• sd – standard deviation of noise parameter

Returns:

outputs of the function

emukit.test_functions.forrester.forrester_low(x, sd=0)

Low fidelity forrester function approximation:

Parameters:

• x – input vector to be evaluated

• sd – standard deviation of observation noise at low fidelity

Returns:

outputs of the function

emukit.test_functions.non_linear_sin.multi_fidelity_non_linear_sin(high_fidelity_noise_std_deviation=0, low_fidelity_noise_std_deviation=0)

Two level non-linear sin function where high fidelity is given by:

\[f_{high}(x) = (x - \sqrt{2}) f_{low}(x)^2\]

and the low fidelity is:

\[f_{low}(x) = \sin(8 \pi x)\]

Reference: Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling. P. Perdikaris, M. Raissi, A. Damianou, N. D. Lawrence and G. E. Karniadakis (2017) http://web.mit.edu/parisp/www/assets/20160751.full.pdf

emukit.test_functions.non_linear_sin.nonlinear_sin_low(x, sd=0)

Low fidelity version of nonlinear sin function

emukit.test_functions.non_linear_sin.nonlinear_sin_high(x, sd=0)

High fidelity version of nonlinear sin function

emukit.test_functions.sixhumpcamel.sixhumpcamel_function()

Two-dimensional SixHumpCamel function, often used as an optimization benchmark.

Based on: https://www.sfu.ca/~ssurjano/camel6.html

\[f(\mathbf{x}) = \left(4-2.1x_1^2 =\]

rac{x_1^4}{3} ight)x_1^2 + x_1x_2 + (-4 +4x_2^2)x_2^2

Module contents