Use of KPLS

from smt.sampling_methods import LHS
from smt.problems import Sphere
from smt.surrogate_models import KPLS
import numpy as np
import otsmt
import openturns as ot

Definition of Initial data

# Construction of the DOE
fun = Sphere(ndim=2)
sampling = LHS(xlimits=fun.xlimits, criterion="m")
xt = sampling(40)
yt = fun(xt)
# Compute the gradient
for i in range(2):
    yd = fun(xt, kx=i)
    yt = np.concatenate((yt, yd), axis=1)

xv = ot.Sample([[0.1,1.],[1.,2.]])

Training of smt model for KPLS

sm_kpls = KPLS(theta0=[1e-2])
sm_kpls.set_training_values(xt, yt[:,0])
sm_kpls.train()

Out:

___________________________________________________________________________

                                   KPLS
___________________________________________________________________________

 Problem size

      # training points.        : 40

___________________________________________________________________________

 Training

   Training ...
   Training - done. Time (sec):  0.0312920

Creation of OpenTurns PythonFunction for prediction

otkpls =  otsmt.smt2ot(sm_kpls)
otkplsprediction = otkpls.getPredictionFunction()
otkplsvariances = otkpls.getConditionalVarianceFunction()
otkplsgradient= otkpls.getPredictionDerivativesFunction()

print('Predicted values by KPLS:',otkplsprediction(xv))
print('Predicted variances values by KPLS:',otkplsvariances(xv))
print('Prediction derivatives by KPLS:',otkplsgradient(xv))

Out:

___________________________________________________________________________

 Evaluation

      # eval points. : 2

   Predicting ...
   Predicting - done. Time (sec):  0.0002170

   Prediction time/pt. (sec) :  0.0001085

Predicted values by KPLS:     [ y0      ]
0 : [ 1.00844 ]
1 : [ 4.99833 ]
Predicted variances values by KPLS:     [ y0          ]
0 : [ 4.57112e-06 ]
1 : [ 4.77084e-06 ]
___________________________________________________________________________

 Evaluation

      # eval points. : 2

   Predicting ...
   Predicting - done. Time (sec):  0.0001779

   Prediction time/pt. (sec) :  0.0000889

___________________________________________________________________________

 Evaluation

      # eval points. : 2

   Predicting ...
   Predicting - done. Time (sec):  0.0001414

   Prediction time/pt. (sec) :  0.0000707

Prediction derivatives by KPLS:     [ y0       y1       ]
0 : [ 0.199663 1.99999  ]
1 : [ 2.00019  3.99988  ]