Use of Least Squares Surrogate Model

from smt.sampling_methods import LHS
from smt.problems import Sphere
from smt.surrogate_models import LS

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 Least Squares

sm_ls = LS()
sm_ls.set_training_values(xt, yt[:,0])
sm_ls.train()

Out:

___________________________________________________________________________

                                    LS
___________________________________________________________________________

 Problem size

      # training points.        : 40

___________________________________________________________________________

 Training

   Training ...
   Training - done. Time (sec):  0.0012939

Creation of OpenTurns PythonFunction for prediction

otls = otsmt.smt2ot(sm_ls)
otlsprediction = otls.getPredictionFunction()

print('Predicted values by LS:',otlsprediction(xv))

Out:

___________________________________________________________________________

 Evaluation

      # eval points. : 2

   Predicting ...
   Predicting - done. Time (sec):  0.0001111

   Prediction time/pt. (sec) :  0.0000556

Predicted values by LS:     [ y0      ]
0 : [ 66.4082 ]
1 : [ 65.3    ]