13.7.11. Macro “modelerbuildGPWithAPriori.py”

13.7.11.1. Objective

This macro is the one described in Deterministic trend and bayesian prior, that creates a gaussian process with a specific trend and an a priori knowledge on the mean and variance of the trend parameters.

13.7.11.2. Macro Uranie

"""
Example of Gaussian Process building with a priori knowledge
"""
import numpy as np
from URANIE import DataServer, Modeler

# Load observations
tdsObs = DataServer.TDataServer("tdsObs", "observations")
tdsObs.fileDataRead("utf_4D_train.dat")

# Construct the GPBuilder
gpb = Modeler.TGPBuilder(tdsObs,         # observations data
                         "x1:x2:x3:x4",  # list of input variables
                         "y",            # output variable
                         "matern3/2",    # name of the correlation function
                         "linear")       # trend defined by a keyword

# Bayesian study
meanPrior = np.array([0.0, 0.0, -1.0, 0.0, -0.1])
covPrior = np.array([1e-4, 0.0, 0.0, 0.0, 0.0,
                     0.0, 1e-4, 0.0, 0.0, 0.0,
                     0.0, 0.0, 1e-4, 0.0, 0.0,
                     0.0, 0.0, 0.0, 1e-4, 0.0,
                     0.0, 0.0, 0.0, 0.0, 1e-4])
gpb.setPriorData(meanPrior, covPrior)

# Search for the optimal hyper-parameters
gpb.findOptimalParameters("ReML",        # optimisation criterion
                          100,           # screening design size
                          "neldermead",  # optimisation algorithm
                          500)           # max. number of optim iterations

# Construct the kriging model
krig = gpb.buildGP()

# Display model information
krig.printLog()

13.7.11.3. Console

This is the result of the last command:

.*******************************
** TKriging::printLog[]
*******************************
 Input Variables:      x1:x2:x3:x4
 Output Variable:      y
 Deterministic trend:  linear
 Trend parameters (5): [3.06586494e-05; 1.64887174e-05; -9.99986787e-01; 1.51959859e-05; -9.99877606e-02 ]
 Correlation function: URANIE::Modeler::TMatern32CorrFunction
 Correlation length:   normalised   (not normalised)
                       2.1450e+00 (2.1438e+00 )
                       1.9092e+00 (1.9090e+00 )
                       2.0062e+00 (2.0040e+00 )
                       8.4315e+00 (8.4390e+00 )

 Variance of the gaussian process:      155.533
 RMSE (by Leave One Out):               0.495448
 Q2:                                    0.852037
*******************************