def test_regression_model():
param_true = np.array([1.0, 2.0]).reshape((1, -1))
from UQpy.run_model.model_execution.PythonModel import PythonModel
model = PythonModel(model_script='pfn_models.py',
model_object_name='model_quadratic',
var_names=['theta_0', 'theta_1'])
h_func = RunModel(model=model)
h_func.run(samples=param_true)
# Add noise
error_covariance = 1.
data_clean = np.array(h_func.qoi_list[0])
noise = Normal(loc=0., scale=np.sqrt(error_covariance)).rvs(
nsamples=4, random_state=1).reshape((4, ))
data_3 = data_clean + noise
candidate_model = ComputationalModel(n_parameters=2,
runmodel_object=h_func,
error_covariance=error_covariance)
optimizer = MinimizeOptimizer(method='nelder-mead')
ml_estimator = MLE(inference_model=candidate_model,
data=data_3,
n_optimizations=1,
random_state=1,
optimizer=optimizer)
assert ml_estimator.mle[0] == 0.8689097631871134
assert ml_estimator.mle[1] == 2.0030767805841143
def test_akmcs_expected_feasibility():
from UQpy.surrogates.kriging.regression_models.LinearRegression import LinearRegression
from UQpy.surrogates.kriging.correlation_models.ExponentialCorrelation import ExponentialCorrelation
marginals = [Normal(loc=0., scale=4.), Normal(loc=0., scale=4.)]
x = MonteCarloSampling(distributions=marginals,
nsamples=20,
random_state=1)
model = PythonModel(model_script='series.py', model_object_name="series")
rmodel = RunModel(model=model)
regression_model = LinearRegression()
correlation_model = ExponentialCorrelation()
K = Kriging(
regression_model=regression_model,
correlation_model=correlation_model,
optimizations_number=10,
correlation_model_parameters=[1, 1],
optimizer=MinimizeOptimizer('l-bfgs-b'),
)
# OPTIONS: 'U', 'EFF', 'Weighted-U'
learning_function = ExpectedFeasibility(eff_a=0,
eff_epsilon=2,
eff_stop=0.001)
a = AdaptiveKriging(distributions=marginals,
runmodel_object=rmodel,
surrogate=K,
learning_nsamples=10**3,
n_add=1,
learning_function=learning_function,
random_state=2)
a.run(nsamples=25, samples=x.samples)
assert a.samples[23, 0] == 1.366058523912817
assert a.samples[20, 1] == -12.914668932772358
def test_rss_runmodel_object():
"""
Check 'runmodel_object' should be a UQpy.RunModel class object.
"""
marginals = [Uniform(loc=0., scale=2.), Uniform(loc=0., scale=1.)]
strata = RectangularStrata(strata_number=[2, 2])
x = TrueStratifiedSampling(distributions=marginals,
strata_object=strata,
nsamples_per_stratum=1,
random_state=1)
from UQpy.surrogates.kriging.regression_models import LinearRegression
from UQpy.surrogates.kriging.correlation_models import ExponentialCorrelation
K = Kriging(
regression_model=LinearRegression(),
correlation_model=ExponentialCorrelation(),
optimizations_number=20,
correlation_model_parameters=[1, 1],
optimizer=MinimizeOptimizer('l-bfgs-b'),
)
model = PythonModel(model_script='python_model_function.py',
model_object_name="y_func")
rmodel = RunModel(model=model)
K.fit(samples=x.samples, values=rmodel.qoi_list)
with pytest.raises(BeartypeCallHintPepParamException):
refinement = GradientEnhancedRefinement(strata=x.strata_object,
runmodel_object='abc',
surrogate=K)
RefinedStratifiedSampling(stratified_sampling=x,
samples_number=6,
samples_per_iteration=2,
refinement_algorithm=refinement)
def test_akmcs_u():
from UQpy.surrogates.kriging.regression_models.LinearRegression import LinearRegression
from UQpy.surrogates.kriging.correlation_models.ExponentialCorrelation import ExponentialCorrelation
marginals = [Normal(loc=0., scale=4.), Normal(loc=0., scale=4.)]
x = MonteCarloSampling(distributions=marginals,
nsamples=20,
random_state=1)
model = PythonModel(model_script='series.py', model_object_name="series")
rmodel = RunModel(model=model)
regression_model = LinearRegression()
correlation_model = ExponentialCorrelation()
K = Kriging(regression_model=regression_model,
correlation_model=correlation_model,
optimizer=MinimizeOptimizer('l-bfgs-b'),
optimizations_number=10,
correlation_model_parameters=[1, 1],
random_state=0)
# OPTIONS: 'U', 'EFF', 'Weighted-U'
learning_function = UFunction(u_stop=2)
a = AdaptiveKriging(distributions=marginals,
runmodel_object=rmodel,
surrogate=K,
learning_nsamples=10**3,
n_add=1,
learning_function=learning_function,
random_state=2)
a.run(nsamples=25, samples=x.samples)
assert a.samples[23, 0] == -4.141979058326188
assert a.samples[20, 1] == -1.6476534435429009
def test_akmcs_samples_error():
from UQpy.surrogates.kriging.regression_models.LinearRegression import LinearRegression
from UQpy.surrogates.kriging.correlation_models.ExponentialCorrelation import ExponentialCorrelation
marginals = [Normal(loc=0., scale=4.), Normal(loc=0., scale=4.)]
x = MonteCarloSampling(distributions=marginals,
nsamples=20,
random_state=0)
model = PythonModel(model_script='series.py', model_object_name="series")
rmodel = RunModel(model=model)
regression_model = LinearRegression()
correlation_model = ExponentialCorrelation()
K = Kriging(regression_model=regression_model,
correlation_model=correlation_model,
optimizer=MinimizeOptimizer('l-bfgs-b'),
optimizations_number=10,
correlation_model_parameters=[1, 1],
random_state=1)
# OPTIONS: 'U', 'EFF', 'Weighted-U'
learning_function = WeightedUFunction(weighted_u_stop=2)
with pytest.raises(NotImplementedError):
a = AdaptiveKriging(distributions=[Normal(loc=0., scale=4.)] * 3,
runmodel_object=rmodel,
surrogate=K,
learning_nsamples=10**3,
n_add=1,
learning_function=learning_function,
random_state=2,
samples=x.samples)
def test_akmcs_expected_improvement_global_fit():
from UQpy.surrogates.kriging.regression_models.LinearRegression import LinearRegression
from UQpy.surrogates.kriging.correlation_models.ExponentialCorrelation import ExponentialCorrelation
marginals = [Normal(loc=0., scale=4.), Normal(loc=0., scale=4.)]
x = MonteCarloSampling(distributions=marginals,
nsamples=20,
random_state=1)
model = PythonModel(model_script='series.py', model_object_name="series")
rmodel = RunModel(model=model)
regression_model = LinearRegression()
correlation_model = ExponentialCorrelation()
K = Kriging(
regression_model=regression_model,
correlation_model=correlation_model,
optimizations_number=10,
correlation_model_parameters=[1, 1],
optimizer=MinimizeOptimizer('l-bfgs-b'),
)
# OPTIONS: 'U', 'EFF', 'Weighted-U'
learning_function = ExpectedImprovementGlobalFit()
a = AdaptiveKriging(distributions=marginals,
runmodel_object=rmodel,
surrogate=K,
learning_nsamples=10**3,
n_add=1,
learning_function=learning_function,
random_state=2)
a.run(nsamples=25, samples=x.samples)
assert a.samples[23, 0] == 11.939859785098493
assert a.samples[20, 1] == -8.429899469300118
def test_vor_gerss():
"""
Test the 6 samples generated by GE-RSS using voronoi stratification
"""
marginals = [Uniform(loc=0., scale=2.), Uniform(loc=0., scale=1.)]
strata_vor = VoronoiStrata(seeds_number=4, dimension=2, random_state=10)
x_vor = TrueStratifiedSampling(
distributions=marginals,
strata_object=strata_vor,
nsamples_per_stratum=1,
)
from UQpy.surrogates.kriging.regression_models.LinearRegression import LinearRegression
from UQpy.surrogates.kriging.correlation_models.ExponentialCorrelation import ExponentialCorrelation
model = PythonModel(model_script='python_model_function.py',
model_object_name="y_func")
rmodel = RunModel(model=model)
K_ = Kriging(regression_model=LinearRegression(),
correlation_model=ExponentialCorrelation(),
optimizations_number=20,
optimizer=MinimizeOptimizer('l-bfgs-b'),
random_state=0,
correlation_model_parameters=[1, 1])
K_.fit(samples=x_vor.samples, values=rmodel.qoi_list)
z_vor = RefinedStratifiedSampling(
stratified_sampling=x_vor,
nsamples=6,
random_state=x_vor.random_state,
refinement_algorithm=GradientEnhancedRefinement(
strata=x_vor.strata_object,
runmodel_object=rmodel,
surrogate=K_,
nearest_points_number=4))
assert np.allclose(
z_vor.samples,
np.array([[1.78345908, 0.01640854], [1.46201137, 0.70862104],
[0.4021338, 0.05290083], [0.1062376, 0.88958226],
[0.61246269, 0.47160095], [1.16609055, 0.30832536]]))
assert np.allclose(
z_vor.samplesU01,
np.array([[0.89172954, 0.01640854], [0.73100569, 0.70862104],
[0.2010669, 0.05290083], [0.0531188, 0.88958226],
[0.30623134, 0.47160095], [0.58304527, 0.30832536]]))
def test_rect_gerss():
"""
Test the 6 samples generated by GE-RSS using rectangular stratification
"""
marginals = [Uniform(loc=0., scale=2.), Uniform(loc=0., scale=1.)]
strata = RectangularStrata(strata_number=[2, 2], random_state=1)
x = TrueStratifiedSampling(distributions=marginals,
strata_object=strata,
nsamples_per_stratum=1)
model = PythonModel(model_script='python_model_function.py',
model_object_name="y_func")
rmodel = RunModel(model=model)
from UQpy.surrogates.kriging.regression_models import LinearRegression
from UQpy.surrogates.kriging.correlation_models import ExponentialCorrelation
K = Kriging(
regression_model=LinearRegression(),
correlation_model=ExponentialCorrelation(),
optimizations_number=20,
random_state=0,
correlation_model_parameters=[1, 1],
optimizer=MinimizeOptimizer('l-bfgs-b'),
)
K.fit(samples=x.samples, values=rmodel.qoi_list)
refinement = GradientEnhancedRefinement(strata=x.strata_object,
runmodel_object=rmodel,
surrogate=K,
nearest_points_number=4)
z = RefinedStratifiedSampling(stratified_sampling=x,
random_state=2,
refinement_algorithm=refinement)
z.run(nsamples=6)
assert np.allclose(
z.samples,
np.array([[0.417022, 0.36016225], [1.00011437, 0.15116629],
[0.14675589, 0.5461693], [1.18626021, 0.67278036],
[1.51296312, 0.77483124], [0.74237455, 0.66026822]]))
import pytest
from UQpy.utilities.MinimizeOptimizer import MinimizeOptimizer
from beartype.roar import BeartypeCallHintPepParamException
from UQpy.surrogates.kriging.Kriging import Kriging
import numpy as np
from UQpy.surrogates.kriging.regression_models import LinearRegression, ConstantRegression
from UQpy.surrogates.kriging.correlation_models import GaussianCorrelation
samples = np.linspace(0, 5, 20).reshape(-1, 1)
values = np.cos(samples)
optimizer = MinimizeOptimizer(method="L-BFGS-B")
krig = Kriging(regression_model=LinearRegression(), correlation_model=GaussianCorrelation(), optimizer=optimizer,
correlation_model_parameters=[0.14], optimize=False, random_state=1)
krig.fit(samples=samples, values=values, correlation_model_parameters=[0.3])
optimizer = MinimizeOptimizer(method="L-BFGS-B")
krig2 = Kriging(regression_model=ConstantRegression(), correlation_model=GaussianCorrelation(), optimizer=optimizer,
correlation_model_parameters=[0.3], bounds=[[0.01, 5]],
optimize=False, optimizations_number=100, normalize=False,
random_state=2)
krig2.fit(samples=samples, values=values)
# Using the in-built linear regression model as a function
linear_regression_model = Kriging(regression_model=LinearRegression(), correlation_model=GaussianCorrelation(), optimizer=optimizer,
correlation_model_parameters=[1]).regression_model
optimizer = MinimizeOptimizer(method="L-BFGS-B")
gaussian_corrleation_model = Kriging(regression_model=LinearRegression(), correlation_model=GaussianCorrelation(), optimizer=optimizer,
correlation_model_parameters=[1]).correlation_model
model = PythonModel(model_script='local_BraninHoo.py',
model_object_name='function')
rmodel = RunModel(model=model)
# %% md
#
# :class:`.Kriging` class defines an object to generate a surrogate model for a given set of data.
# %%
from UQpy.surrogates.gaussian_process.regression_models import LinearRegression
from UQpy.surrogates.gaussian_process.kernels import RBF
bounds = [[10**(-3), 10**3], [10**(-3), 10**2], [10**(-3), 10**2]]
optimizer = MinimizeOptimizer(method="L-BFGS-B", bounds=bounds)
K = GaussianProcessRegression(regression_model=LinearRegression(),
kernel=RBF(),
optimizer=optimizer,
hyperparameters=[1, 1, 0.1],
optimizations_number=10)
# %% md
#
# Choose an appropriate learning function.
# %%
from UQpy.sampling.adaptive_kriging_functions.ExpectedImprovement import ExpectedImprovement
# %% md
n_parameters=i + 1,
name=names[i],
error_covariance=error_covariance)
estimators.append(MLE(inference_model=M, data=data_1))
#%% md
#
# Apart from the data, candidate models and method (:class:`.BIC`, :class:`.AIC`...),
# :class:`.InformationModelSelection` also takes as inputs lists of
# inputs to the maximum likelihood class. Those inputs should be lists of length
# len(candidate_models).
#%%
from UQpy.utilities.MinimizeOptimizer import MinimizeOptimizer
optimizer = MinimizeOptimizer(method='nelder-mead')
selector = InformationModelSelection(parameter_estimators=estimators,
criterion=BIC(),
n_optimizations=[1] * 3)
selector.sort_models()
print('Sorted models: ', [m.name for m in selector.candidate_models])
print('Values of criterion: ', selector.criterion_values)
print('Values of data fit:', [
cr - pe
for (cr, pe) in zip(selector.criterion_values, selector.penalty_terms)
])
print('Values of penalty term (complexity):', selector.penalty_terms)
print('Values of model probabilities:', selector.probabilities)
#%% md
#
# RunModel is used to evaluate function values at sample points. Model is defined as a function in python file
# 'python_model_function.py'.
# %%
model = PythonModel(model_script='local_python_model_1Dfunction.py',
model_object_name='y_func',
delete_files=True)
rmodel = RunModel(model=model)
rmodel.run(samples=x.samples)
from UQpy.surrogates.gaussian_process.regression_models import LinearRegression
from UQpy.utilities.MinimizeOptimizer import MinimizeOptimizer
bounds = [[10**(-3), 10**3], [10**(-3), 10**2]]
optimizer = MinimizeOptimizer(method='L-BFGS-B', bounds=bounds)
K = GaussianProcessRegression(regression_model=LinearRegression(),
kernel=RBF(),
optimizer=optimizer,
optimizations_number=20,
hyperparameters=[1, 0.1],
random_state=2)
K.fit(samples=x.samples, values=rmodel.qoi_list)
print(K.hyperparameters)
# %% md
#
# RunModel is used to evaluate function values at sample points. Model is defined as a function in python file
# 'python_model_function.py'.