Cooperative Components Kriging (CoopCompKRG)

Cooperative Components Kriging is a way of fitting a high-dimensional ordinary Kriging model by sequential lower-dimensional component model fits. For each component, only the associated hyperparameters are optimized. All other hyperparameters are set to a so-called cooperative context vector, which contains the current best hyperparameter values.

This application contains the single component model fits. The loop over the components has to be implemented individually, as shown in the usage example below.

The cooperative components model fit was developed as part of a high-dimensional surrogate-based optimization process. It is inspired by distributed multi-disciplinary design optimization (MDO) approaches and the cooperative EGO by Zhan et al. [1].

References

[1]

Zhan, D., Wu, J., Xing, H. et al., A cooperative approach to efficient global optimization. J Glob Optim 88, 327–357 (2024).

Usage

import numpy as np

from smt.surrogate_models import CoopCompKRG
from smt.problems import TensorProduct
from smt.sampling_methods import LHS

# The problem is the exponential problem with dimension 10
ndim = 10
prob = TensorProduct(ndim=ndim, func="exp")

# Example with three random components
ncomp = 3

# Initial sampling
samp = LHS(xlimits=prob.xlimits, seed=42)
xt = samp(50)
yt = prob(xt)

# Cooperative components Kriging model fit
# comp_var is auto-computed from ncomp and seed
sm = CoopCompKRG(ncomp=ncomp)
sm.set_training_values(xt, yt)
sm.train()

# Prediction as for ordinary Kriging
xpoint = (-5 + np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]])) / 10.0
print(sm.predict_values(xpoint))
print(sm.predict_variances(xpoint))

___________________________________________________________________________

                      Cooperative Components Kriging
___________________________________________________________________________

 Problem size

      # training points.        : 50

___________________________________________________________________________

 Training

   Training ...
   Training - done. Time (sec):  2.1547103
___________________________________________________________________________

 Evaluation

      # eval points. : 1

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

   Prediction time/pt. (sec) :  0.0000000

[[0.42716488]]
[[6.5016309]]

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	[‘pow_exp’, ‘abs_exp’, ‘squar_exp’, ‘squar_sin_exp’, ‘matern52’, ‘matern32’]	[‘str’]	Correlation function type
pow_exp_power	1.9	None	[‘float’]	Power for the pow_exp kernel function (valid values in (0.0, 2.0]). This option is set automatically when corr option is squar, abs, or matern.
categorical_kernel	MixIntKernelType.CONT_RELAX	[<MixIntKernelType.CONT_RELAX: ‘CONT_RELAX’>, <MixIntKernelType.GOWER: ‘GOWER’>, <MixIntKernelType.EXP_HOMO_HSPHERE: ‘EXP_HOMO_HSPHERE’>, <MixIntKernelType.HOMO_HSPHERE: ‘HOMO_HSPHERE’>, <MixIntKernelType.COMPOUND_SYMMETRY: ‘COMPOUND_SYMMETRY’>, <MixIntKernelType.DIST_ENCODING: ‘DIST_ENCODING’>]	None	The kernel to use for categorical inputs. Only for non continuous Kriging
categorical_kernel_beta	1.0	None	[‘float’, ‘int’]	Power for the distributional encoding kernel (valid values in (0.0, 2.0]).
hierarchical_kernel	MixHrcKernelType.ALG_KERNEL	[<MixHrcKernelType.ALG_KERNEL: ‘ALG_KERNEL’>, <MixHrcKernelType.ARC_KERNEL: ‘ARC_KERNEL’>]	None	The kernel to use for mixed hierarchical inputs. Only for non continuous Kriging
nugget	2.220446049250313e-14	None	[‘float’]	a jitter for numerical stability
theta0	[0.01]	None	[‘list’, ‘ndarray’]	Initial hyperparameters
theta_bounds	[1e-06, 20.0]	None	[‘list’, ‘ndarray’]	bounds for hyperparameters
hyper_opt	Cobyla	[‘Cobyla’]	[‘str’]	Optimizer for hyperparameters optimisation
eval_noise	False	[True, False]	[‘bool’]	noise evaluation flag
noise0	[0.0]	None	[‘list’, ‘ndarray’]	Initial noise hyperparameters
noise_bounds	[np.float64(2.220446049250313e-14), 10000000000.0]	None	[‘list’, ‘ndarray’]	bounds for noise hyperparameters
use_het_noise	False	[True, False]	[‘bool’]	heteroscedastic noise evaluation flag
n_start	10	None	[‘int’]	number of optimizer runs (multistart method)
xlimits	None	None	[‘list’, ‘ndarray’]	definition of a design space of float (continuous) variables: array-like of size nx x 2 (lower, upper bounds)
design_space	None	None	[‘BaseDesignSpace’, ‘list’, ‘ndarray’]	definition of the (hierarchical) design space: use smt.design_space.DesignSpace as the main API. Also accepts list of float variable bounds
is_ri	False	None	[‘bool’]	activate reinterpolation for noisy cases
seed	41	None	[‘NoneType’, ‘int’, ‘Generator’]	Numpy Generator object or seed number which controls random draws for internal optim (set by default to get reproductibility)
comp_var	None	None	None	Boolean array [nx, n_comp] mapping design variables to components. If None, computed automatically from ncomp and seed.
ncomp	3	None	[‘int’]	Number of components (used to build comp_var when not provided)