Using pyKriging

pyKriging was designed to simply the process of creating surrogate models. The following example demonstrates how to create a sampling plan, evaluate a test function at those locations, create and train a Kriging model and add infill points to reduce the models Mean Squared Error (MSE).

import pyKriging  
from pyKriging.krige import kriging  
from pyKriging.samplingplan import samplingplan

# The Kriging model starts by defining a sampling plan, we use an optimal Latin Hypercube here
sp = samplingplan(2)  
X = sp.optimallhc(20)

# Next, we define the problem we would like to solve
testfun = pyKriging.testfunctions().branin  
y = testfun(X)

# Now that we have our initial data, we can create an instance of a Kriging model
k = kriging(X, y, testfunction=testfun, name='simple')  
k.train()

# Now, five infill points are added. Note that the model is re-trained after each point is added
numiter = 5  
for i in range(numiter):  
    print 'Infill iteration {0} of {1}....'.format(i + 1, numiter)
    newpoints = k.infill(1)
    for point in newpoints:
        k.addPoint(point, testfun(point)[0])
    k.train()

# And plot the results
k.plot()  

The result of this script should produce the following output. Your model may vary slightly, as pyKriging extensively uses Stochastic optimization to build these models.