y = g(inputSample)
outputObservationNoiseSigma = 0.05
meanNoise = ot.Point(outputDimension)
covarianceNoise = ot.Point(outputDimension, outputObservationNoiseSigma)
R = ot.IdentityMatrix(outputDimension)
observationOutputNoise = ot.Normal(meanNoise, covarianceNoise, R)
# Add noise
sampleNoise = observationOutputNoise.getSample(size)
y += sampleNoise
candidate = [1.0] * 3
bootstrapSizes = [0, 100]
for bootstrapSize in bootstrapSizes:
algo = ot.NonLinearLeastSquaresCalibration(model, x, y, candidate)
algo.setBootstrapSize(bootstrapSize)
algo.run()
# To avoid discrepance between the plaforms with or without CMinpack
# Check MAP
calibrationResult = algo.getResult()
parameterMAP = calibrationResult.getParameterMAP()
print("(Auto) MAP=", repr(parameterMAP))
rtol = 1.0e-2
atol = 0.0
ott.assert_almost_equal(parameterMAP, trueParameter, rtol, atol)
algo.setOptimizationAlgorithm(
ot.MultiStart(
ot.TNC(),
ot.LowDiscrepancyExperiment(
ot.SobolSequence(),
# %% # There are several methods to solve the problem. # # * Given that the problem is not identifiable, we can use some regularization method. Two methods are provided in the library: the Gaussian linear least squares `GaussianLinearCalibration` and the Gaussian non linear least squares `GaussianNonlinearCalibration`. # * We can change the problem, replacing it with a problem which is identifiable. In the flooding model, we can view :math:`Z_v` and :math:`Z_m` as constants and calibrate :math:`K_s` only. # %% # Calibration with non linear least squares # ----------------------------------------- # %% # The `NonLinearLeastSquaresCalibration` class performs the non linear least squares calibration by minimizing the squared euclidian norm between the predictions and the observations. # %% algo = ot.NonLinearLeastSquaresCalibration(mycf, Qobs, Hobs, thetaPrior) # %% # The `run` method computes the solution of the problem. # %% algo.run() # %% calibrationResult = algo.getResult() # %% # Analysis of the results # ----------------------- # %%
#
# Moreover, the distribution of the residuals is close to being gaussian.
# %%
graph = calibrationResult.drawParameterDistributions()
view = viewer.View(graph)
# %%
# Calibration with nonlinear least squares
# ----------------------------------------
# %%
# The `NonLinearLeastSquaresCalibration` class performs the non linear least squares calibration by minimizing the squared euclidian norm between the predictions and the observations.
# %%
algo = ot.NonLinearLeastSquaresCalibration(mycf, observedStrain,
observedStress, thetaPrior)
# %%
# The `run` method computes the solution of the problem.
# %%
algo.run()
# %%
calibrationResult = algo.getResult()
# %%
# Analysis of the results
# -----------------------
# %%
