GPX

GPX is a rewrite of Kriging (aka KRG) and KPLS models of SMT in Rust. Actually GPX is a wrapper of the Gpx model from the egobox library which is adapted here to the surrogate models API of SMT.

If you find the performances of the Python implementation (training/prediction time) not sufficient for your use case, you may want to give GPX a try.

You will need to install the egobox extra dependency with the command: pip install smt[gpx]

More information about the egobox library can be found in [1].

Limitations

• wrt KRG/KPLS: GPX does not implement mixed integer or hierarchical variables, derivatives, noise handling or KRG sampling.

• wrt egobox::Gpx: GPX does not give access to mixture of gaussian processes, does not give access to GP sampling

See [2] for more information on egobox::Gpx.

Reference

[1]

Lafage, R., (2022). egobox, a Rust toolbox for efficient global optimization. Journal of Open Source Software, 7(78), 4737,

[2]

Tutorial egobox::Gpx

Usage

Example

import numpy as np
import matplotlib.pyplot as plt

from smt.surrogate_models import GPX

xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
yt = np.array([0.0, 1.0, 1.5, 0.9, 1.0])

sm = GPX(theta0=[1e-2])
sm.set_training_values(xt, yt)
sm.train()

num = 100
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
# estimated variance
s2 = sm.predict_variances(x)

_, axs = plt.subplots(1)
# add a plot with variance
axs.plot(xt, yt, "o")
axs.plot(x, y)
axs.fill_between(
    np.ravel(x),
    np.ravel(y - 3 * np.sqrt(s2)),
    np.ravel(y + 3 * np.sqrt(s2)),
    color="lightgrey",
)
axs.set_xlabel("x")
axs.set_ylabel("y")
axs.legend(
    ["Training data", "Prediction", "Confidence Interval 99%"],
    loc="lower right",
)

plt.show()

___________________________________________________________________________

                                    GPX
___________________________________________________________________________

 Problem size

      # training points.        : 5

___________________________________________________________________________

 Training

   Training ...
   Training - done. Time (sec):  0.0085671
___________________________________________________________________________

 Evaluation

      # eval points. : 100

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

Options

List of options

Option	Default	Acceptable values	Acceptable types	Description
print_global	True	None	[‘bool’]	Global print toggle. If False, all printing is suppressed
print_training	True	None	[‘bool’]	Whether to print training information
print_prediction	True	None	[‘bool’]	Whether to print prediction information
print_problem	True	None	[‘bool’]	Whether to print problem information
print_solver	True	None	[‘bool’]	Whether to print solver information
poly	constant	[‘constant’, ‘linear’, ‘quadratic’]	[‘str’]	Regression function type
corr	squar_exp	[‘abs_exp’, ‘squar_exp’, ‘matern32’, ‘matern52’]	None	Correlation function type
theta0	[0.01]	None	[‘list’, ‘ndarray’]	Initial hyperparameters
theta_bounds	[1e-06, 20.0]	None	[‘list’, ‘ndarray’]	Bounds for hyperparameters
n_start	10	None	[‘int’]	Number of optimizer runs (multistart method)
kpls_dim	None	None	[‘NoneType’, ‘int’]	Number of PLS components used for dimension reduction
seed	42	None	[‘int’]	Seed number which controls random draws for internal optim (set by default to get reproductibility)