kriging.py

Surrogate model based on Kriging.

class openmdao.surrogate_models.kriging.KrigingSurrogate(**kwargs)

Bases: SurrogateModel

Surrogate Modeling method based on the simple Kriging interpolation.

Predictions are returned as a tuple of mean and RMSE. Based on Gaussian Processes for Machine Learning (GPML) by Rasmussen and Williams. (see also: scikit-learn).

Parameters:

**kwargsdict

Options dictionary.

Attributes:

alphandarray

Reduced likelihood parameter: alpha

Lndarray

Reduced likelihood parameter: L

n_dimsint

Number of independents in the surrogate

n_samplesint

Number of training points.

sigma2ndarray

Reduced likelihood parameter: sigma squared

thetasndarray

Kriging hyperparameters.

Xndarray

Training input values, normalized.

X_meanndarray

Mean of training input values, normalized.

X_stdndarray

Standard deviation of training input values, normalized.

Yndarray

Training model response values, normalized.

Y_meanndarray

Mean of training model response values, normalized.

Y_stdndarray

Standard deviation of training model response values, normalized.

_minimizefunction

Lazily imported scipy.optimize.minimize function.

__init__(**kwargs)

Initialize all attributes.

Parameters:

**kwargsdict

options dictionary.

linearize(x)

Calculate the jacobian of the Kriging surface at the requested point.

Parameters:

xarray-like

Point at which the surrogate Jacobian is evaluated.

Returns:

ndarray

Jacobian of surrogate output wrt inputs.

predict(x)

Calculate predicted value of the response based on the current trained model.

Parameters:

xarray-like

Point at which the surrogate is evaluated.

Returns:

ndarray

Kriging prediction.

ndarray, optional (if eval_rmse is True)

Root mean square of the prediction error.

train(x, y, verbose=False, method='SLSQP', **minimize_options)

Train the surrogate model with the given set of inputs and outputs.

Additional options for the internal hyperparameter training with scipy.optimize.minimize can be passed as keyword arguments.

The default options passed are {‘tol’: 1e-3, ‘maxiter’: 50}.

Parameters:

xarray-like

Training input locations.

yarray-like

Model responses at given inputs.

verbosebool, optional

Print internal minimization results and post-training data for debugging.

methodstr, optional

Optimization method to use for hyperparameter tuning. Default is ‘L-BFGS-B’, which is the standard for Kriging/Gaussian processes. Other options include ‘SLSQP’, ‘TNC’, etc.

**minimize_optionsdict

Additional options passed to scipy.optimize.minimize.

vectorized_predict(x)

Calculate predicted values of the response based on the current trained model.

Parameters:

xarray-like

Vectorized point(s) at which the surrogate is evaluated.