Hi,
You can split your database into a learning part and a validation part (or test
part), then use the first part to build the metamodel and the second one to
assess its quality. I have modified your script to illustrate the point. Feel
free to contact me directly if you need further assistance.
Cheers
Régis
import openturns as ot
# ==============
# Read the design of experiments samples (5 columns for x1,x2,x3,x4,x5)
# and response variables (1 column)
# ==============
inputSample = ot.Sample.ImportFromCSVFile('InputSamples.csv',',')
y1 = ot.Sample.ImportFromCSVFile('OutputSamples.csv',',')
# ==============
# Split your database in two parts: learning/test
# ==============
ratio = 0.1 # 10% of the database to test the accuracy
testX = inputSample.split(int(ratio * size))
testY = y1.split(int(ratio * size))
# ==============
# Construct a kriging metamodel
# ==============
dimension = inputSample.getDimension()
basis = ot.ConstantBasisFactory(dimension).build()
covarianceModel = ot.SquaredExponential([1.]*dimension, [1.0])
algo = ot.KrigingAlgorithm(inputSample, y1, covarianceModel, basis)
algo.run()
result = algo.getResult()
krigingMetamodel = result.getMetaModel()
print(result.getTrendCoefficients())
print(result.getCovarianceModel())
# ==============
# Perform assessment of the quality of the metamodel constructed
# ==============
validation = ot.MetaModelValidation(testX, testY, krigingMetamodel)
print("predictivity factor=", validation.computePredictivityFactor())
graph = validation.drawValidation()
ot.Show(graph)
graph = validation.getResidualDistribution().drawPDF()
graph.setXTitle("Residuals")
ot.Show(graph)
Le jeudi 26 mars 2020 à 21:17:21 UTC+1, Aytekin Gel <[email protected]> a écrit :
Hello,
I just started exploring OpenTURNS, which seems to be a quite powerful UQ
toolbox with advanced features implemented. Thanks for offering it to the users
worldwide.
I wanted seek help regarding few tasks in spite of my efforts to find similar
examples.
I have a quite expensive computational fluid dynamics simulations (multiphase
flow), which requires building a surrogate model (metamodel) in order to
perform other uncertainty quantification analysis.
I conducted by generating an optimal Latin Hypercube based sampling for 5 input
parameters (x1, ..., x5) and one scalar response variables or quantities of
interest (y1) using other tools extrernally.
I am trying to perform several tasks as listed below with OpenTURNS:
(1) construct a kriging metamodel and and assess the adequacy of the metamodel
preferably with cross-validation error assessment or some other statistical
measure.
(2) perform sensitivity analysis using ANCOVA as my input parameters are
correlated such that x1= 1- (x2+x3+x4+x5) and each of the inputs have a certain
range of lower and upper bounds.
Reviewing the available examples, I think I was able to generate the kriging
metamodel as shown at the end of my email. However, I couldn't figure out how
to perform cross-validation or assessment of the adequacy of the metamodel.
All of the examples that I was able to find appears to have an explicit model
defined algebraically such as in the Kriging the cantilever beam model:
model = ot.SymbolicFunction(["E", "F", "L", "I"], ["F*L^3/(3*E*I)"])
In my case, I don't have an explicit model definition so could you please help
me showing an example on how to assess the adequacy of the metamodel
constructed? I found the following information but again there was explicit
definition for model and metamodel:
http://openturns.github.io/openturns/master/user_manual/response_surface/_generated/openturns.MetaModelValidation.html#openturns-metamodelvalidation
My example that I have generated:
---------------------------------------------------------------------
import openturns as ot
# ==============
# Read the design of experiments samples (5 columns for x1,x2,x3,x4,x5)
# and response variables (1 column)
# ==============
inputSample = ot.Sample.ImportFromCSVFile('InputSamples.csv',',')
y1 = ot.Sample.ImportFromCSVFile('OutputSamples.csv',',')
# ==============
# Construct a kriging metamodel
# ==============
dimension = inputSample.getDimension()
basis = ot.ConstantBasisFactory(dimension).build()
covarianceModel = ot.SquaredExponential([1.]*dimension, [1.0])
algo = ot.KrigingAlgorithm(inputSample, y1, covarianceModel, basis)
algo.run()
result = algo.getResult()
krigingMetamodel = result.getMetaModel()
print(result.getTrendCoefficients())
print(result.getCovarianceModel())
# ==============
# Perform assessment of the quality of the metamodel constructed
# ==============
x1_dist = ot.Uniform(0.2088,0.6975)
x1_dist.setDescription("x1")
x2_dist = ot.Uniform(0.0015,0.499)
x2_dist.setDescription("x2")
x3_dist = ot.Uniform(0.00164,0.4985)
x3_dist.setDescription("x3")
x4_dist = ot.Uniform(2.3921e-5,0.0998)
x4_dist.setDescription("x4")
x5_dist = ot.Uniform(0.000267,0.0999)
x5_dist.setDescription("x5")
myDistribution = ot.ComposedDistribution([x1_dist, x2_dist, x3_dist, x4_dist,
x5_dist])
sampleSize_test = 100
<.... assess the adequacy of the metamodel constructed ...>
---------------------------------------------------------------------
Could you please let me know how can I perform quality check of the metamodel
built in the above example? Then I will try to use example ANCOVA to perform
sensitivity analysis using the metamodel constructed in the above example.
Thank you very much for your help and time, and my apologies for the long email.
Aytekin Gel, Ph.D.
--
Aytekin Gel, Ph.D.
Manager,
ALPEMI Consulting, LLC
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