[ot-users] gPC generation: seperate training set calculations and generation of the polynomial

BLATMAN Geraud geraud.blatman at edf.fr
Wed Jan 25 14:43:47 CET 2017


Hi François,


I begin with your 2nd question. Yes it is possible to train the metamodel based only on the input and the output data sets. Indeed, a possible usage of ``FunctionalChaosAlgorithm`` is as follows:

FunctionalChaosAlgorithm(inputSample, outputSample, distribution, adaptiveStrategy)

Note that this usage requires the knowledge of the probability distribution (argument ``distribution``) of your inputs. You may have a look at the doc<http://doc.openturns.org/openturns-1.5/sphinx/user_manual/_generated/openturns.FunctionalChaosAlgorithm.html> and adapt the example located at the bottom of the page.


This way it is easy to construct a polynomial chaos from a training set and to validate it based on a separated validation set. Here are a few commands (partially based on the ``numpy`` module) which you may use to this purpose:


>>> import numpy as np

>>> import openturns as ot

>>> from openturns.viewer import View

>>>

>>> # Import input and output data sets as OT Numerical Samples

>>> inputs = ot.NumericalSample.ImportFromCSVFile("my_inputs.txt")

>>> outputs = ot.NumericalSample.ImportFromCSVFile("my_outputs.txt")

>>>

>>> # Convert them to numpy arrays to allow easy manipulations

>>> inputs_arr, outputs_arr = np.array(inputs), np.array(outputs)

>>>

>>> # Randomly split the data into training and validation sets

>>> np.random.seed(10) # set the random generator seed

>>> n = inputs.getDimension()

>>> fraction_train = 0.7 # proportion of points used for training

>>> n_train = int(n*fraction_train) # number of training points

>>> inds = np.random.permutation(n)
>>> xs, ys = x[inds,:], y[inds,:]
>>> x_train, x_valid = xs[:n_train, :], xs[n_train:, :]
>>> y_train, y_valid = ys[:n_train, :], ys[n_train:, :]

>>>

(... polynomial chaos command lines ...)

>>> algo = ot.FunctionalChaosAlgorithm(x_train, y_train, distribution, fixedStrategy, self.projectionStrategy)

>>> algo.run()

>>> result = algo.getResult()

>>>

>>> # Validate the metamodel

>>> valid = ot.MetaModelValidation(x_train, y_train, result.getMetaModel())
>>> self.relative_accuracy = valid.computePredictivityFactor()
>>> graph = valid.drawValidation()

>>> View(graph)


Regards,


Géraud


________________________________
De : users-bounces at openturns.org <users-bounces at openturns.org>
Envoyé : mercredi 25 janvier 2017 11:08
À : users at openturns.org
Objet : [ot-users] gPC generation: seperate training set calculations and generation of the polynomial

Hello everyone,
I am new to OT and I would like to make a polynomial approximation of an expensive function. For that I would like first to evaluate the function at the colocation points and then train my polynomial.
In the example in OT, those two steps are not separated. However is there a way to run them separately ?
Alternatively, assuming I already have the training set (colocation points and the corresponding function value) is it possible to train the polynomial with OT winthout having OT to evaluate the expensive function (with the function FunctionalChaosAlgorithm.run()) ?

Thanks a lot

Francois Sanson



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