def multi_fidelity_borehole_function(high_noise_std_deviation=0, low_noise_std_deviation=0):
"""
Two level borehole function.
The Borehole function models water flow through a borehole. Its simplicity and quick evaluation makes it a commonly
used function for testing a wide variety of methods in computer experiments.
See reference for equations:
https://www.sfu.ca/~ssurjano/borehole.html
:param high_noise_std_deviation: Standard deviation of Gaussian observation noise on high fidelity observations.
Defaults to zero.
:param low_noise_std_deviation: Standard deviation of Gaussian observation noise on low fidelity observations.
Defaults to zero.
:return: Tuple of user function object and parameter space
"""
parameter_space = ParameterSpace([
ContinuousParameter('borehole_radius', 0.05, 0.15),
ContinuousParameter('radius_of_influence', 100, 50000),
ContinuousParameter('upper_aquifer_transmissivity', 63070, 115600),
ContinuousParameter('upper_aquifer_head', 990, 1110),
ContinuousParameter('lower_aquifer_transmissivity', 63.1, 116),
ContinuousParameter('lower_aquifer_head', 700, 820),
ContinuousParameter('borehole_length', 1120, 1680),
ContinuousParameter('hydraulic_conductivity', 9855, 12045),
InformationSourceParameter(2)])
user_function = MultiSourceFunctionWrapper([
lambda x: borehole_low(x, low_noise_std_deviation),
lambda x: borehole_high(x, high_noise_std_deviation)])
return user_function, parameter_space
def 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:
.. math::
f_{high}(x) = (x - \sqrt{2}) f_{low}(x)^2
and the low fidelity is:
.. math::
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
"""
parameter_space = ParameterSpace(
[ContinuousParameter("x1", -5, 10),
InformationSourceParameter(2)])
user_function = MultiSourceFunctionWrapper([
lambda x: nonlinear_sin_low(x, low_fidelity_noise_std_deviation),
lambda x: nonlinear_sin_high(x, high_fidelity_noise_std_deviation),
])
return user_function, parameter_space
def multi_source_entropy_search_acquisition(gpy_model):
space = ParameterSpace(
[ContinuousParameter("x1", 0, 1),
InformationSourceParameter(2)])
return MultiInformationSourceEntropySearch(gpy_model,
space,
num_representer_points=10)
def multi_source_optimizer():
mock_acquisition_optimizer = mock.create_autospec(AcquisitionOptimizer)
mock_acquisition_optimizer.optimize.return_value = (np.array([[0.]]), None)
space = ParameterSpace(
[ContinuousParameter('x', 0, 1),
InformationSourceParameter(2)])
return MultiSourceAcquisitionOptimizer(mock_acquisition_optimizer, space)
def 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:
.. math::
f(x) = (6x - 2)^2 \sin(12x - 4)
and the low fidelity approximation given by:
.. math::
f_{low}(x) = 0.5 f_{high}(x) + 10 (x - 0.5) + 5
:param high_fidelity_noise_std_deviation: Standard deviation of observation noise on high fidelity observations.
Defaults to zero.
:param low_fidelity_noise_std_deviation: Standard deviation of observation noise on low fidelity observations.
Defaults to zero.
:return: Tuple of user function object and parameter space object
"""
parameter_space = ParameterSpace([ContinuousParameter("x", 0, 1), InformationSourceParameter(2)])
user_function = MultiSourceFunctionWrapper(
[
lambda x: forrester_low(x, low_fidelity_noise_std_deviation),
lambda x: forrester(x, high_fidelity_noise_std_deviation),
]
)
return user_function, parameter_space
def test_random_search_acquisition_optimizer_with_context(simple_square_acquisition):
space = ParameterSpace([CategoricalParameter('x', OrdinalEncoding(np.arange(0, 100))),
InformationSourceParameter(10)])
optimizer = RandomSearchAcquisitionOptimizer(space, 1000)
source_encoding = 1
opt_x, opt_val = optimizer.optimize(simple_square_acquisition, {'source': source_encoding})
assert_array_equal(opt_x, np.array([[1., source_encoding]]))
assert_array_equal(opt_val, np.array([[0. + source_encoding]]))
def test_multi_source_acquisition_optimizer(simple_square_acquisition):
space = ParameterSpace(
[ContinuousParameter("x", 0, 1),
InformationSourceParameter(2)])
single_optimizer = GradientAcquisitionOptimizer(space)
optimizer = MultiSourceAcquisitionOptimizer(single_optimizer, space)
opt_x, opt_val = optimizer.optimize(simple_square_acquisition)
assert_array_equal(opt_x, np.array([[0.0, 1.0]]))
assert_array_equal(opt_val, np.array([[2.0]]))
def test_multi_source_acquisition_optimizer():
space = ParameterSpace(
[ContinuousParameter('x', 0, 1),
InformationSourceParameter(2)])
acquisition = SimpleSquareAcquisition()
single_optimizer = AcquisitionOptimizer(space)
optimizer = MultiSourceAcquisitionOptimizer(single_optimizer, space)
opt_x, opt_val = optimizer.optimize(acquisition)
np.testing.assert_array_equal(opt_x, np.array([[0., 1.]]))
np.testing.assert_array_equal(opt_val, np.array([[2.]]))
def test_local_search_acquisition_optimizer_with_context(
simple_square_acquisition):
space = ParameterSpace([
CategoricalParameter("x", OrdinalEncoding(np.arange(0, 100))),
InformationSourceParameter(10)
])
optimizer = LocalSearchAcquisitionOptimizer(space, 1000, 3)
source_encoding = 1
opt_x, opt_val = optimizer.optimize(simple_square_acquisition,
{"source": source_encoding})
np.testing.assert_array_equal(opt_x, np.array([[1.0, source_encoding]]))
np.testing.assert_array_equal(opt_val, np.array([[0.0 + source_encoding]]))
def test_multi_source_sequential_with_source_context():
# Check that we can fix a non-information source parameter with context
mock_acquisition = mock.create_autospec(Acquisition)
mock_acquisition.has_gradients = False
mock_acquisition.evaluate = lambda x: np.sum(x**2, axis=1)[:, None]
space = ParameterSpace(
[ContinuousParameter("x", 0, 1), ContinuousParameter("y", 0, 1), InformationSourceParameter(2)]
)
acquisition_optimizer = GradientAcquisitionOptimizer(space)
multi_source_acquisition_optimizer = MultiSourceAcquisitionOptimizer(acquisition_optimizer, space)
loop_state_mock = mock.create_autospec(LoopState)
seq = SequentialPointCalculator(mock_acquisition, multi_source_acquisition_optimizer)
next_points = seq.compute_next_points(loop_state_mock, context={"source": 1.0})
# "SequentialPointCalculator" should only ever return 1 value
assert len(next_points) == 1
# Context value should be what we set
assert np.isclose(next_points[0, 1], 1.0)
def test_two_information_source_parameters_fail():
with pytest.raises(ValueError):
ParameterSpace(
[InformationSourceParameter(2),
InformationSourceParameter(2)])
def MUMBO_acquisition(gpy_model):
space = ParameterSpace(
[ContinuousParameter("x1", 0, 1),
InformationSourceParameter(2)])
return MUMBO(gpy_model, space, num_samples=10, grid_size=5000)
def test_single_value_in_domain_information_source_parameter():
param = InformationSourceParameter(5)
assert param.check_in_domain(2) is True
assert param.check_in_domain(7) is False
def test_information_source_parameter():
param = InformationSourceParameter(5)
assert param.name == 'source'
assert param.check_in_domain(np.array([0, 1])) is True
assert param.check_in_domain(np.array([4])) is True
assert param.check_in_domain(np.array([5])) is False
def test_single_value_in_domain_information_source_parameter():
param = InformationSourceParameter(5)
assert param.check_in_domain(2) is True
assert param.check_in_domain(7) is False
def test_information_source_parameter():
param = InformationSourceParameter(5)
assert param.name == 'source'
assert param.check_in_domain(np.array([0, 1])) is True
assert param.check_in_domain(np.array([4])) is True
assert param.check_in_domain(np.array([5])) is False