kriging.py

Surrogate model based on Kriging.

class openmdao.surrogate_models.kriging.FloatKrigingSurrogate(nugget=2.2204460492503131e-15, eval_rmse=False)[source]

Bases: openmdao.surrogate_models.kriging.KrigingSurrogate

Surrogate model based on the simple Kriging interpolation.

Predictions are returned as floats, which are the mean of the model’s prediction.

__init__(nugget=2.2204460492503131e-15, eval_rmse=False)

Initialize all attributes.

Parameters:

nugget : double or ndarray, optional

Nugget smoothing parameter for smoothing noisy data. Represents the variance of the input values. If nugget is an ndarray, it must be of the same length as the number of training points. Default: 10. * Machine Epsilon

eval_rmse : bool

Flag indicating whether the Root Mean Squared Error (RMSE) should be computed. Set to False by default.

linearize(x)

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

Parameters:

x : array-like

Point at which the surrogate Jacobian is evaluated.

Returns:

ndarray

Jacobian of surrogate output wrt inputs.

predict(x)[source]

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

Parameters:

x : array-like

Point at which the surrogate is evaluated.

Returns:

float

Mean value of kriging prediction.

train(x, y)

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

Parameters:

x : array-like

Training input locations

y : array-like

Model responses at given inputs.

vectorized_predict(x)

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

Parameters:

x : array-like

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

class openmdao.surrogate_models.kriging.KrigingSurrogate(nugget=2.2204460492503131e-15, eval_rmse=False)[source]

Bases: openmdao.surrogate_models.surrogate_model.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).

Attributes

alpha (ndarray) Reduced likelyhood parameter: alpha
eval_rmse (bool) When true, calculate the root mean square prediction error.
L (ndarray) Reduced likelyhood parameter: L
n_dims (int) Number of independents in the surrogate
n_samples (int) Number of training points.
nugget (double or ndarray, optional) Nugget smoothing parameter for smoothing noisy data. Represents the variance of the input values. If nugget is an ndarray, it must be of the same length as the number of training points. Default: 10. * Machine Epsilon
sigma2 (ndarray) Reduced likelyhood parameter: sigma squared
thetas (ndarray) Kriging hyperparameters.
X (ndarray) Training input values, normalized.
X_mean (ndarray) Mean of training input values, normalized.
X_std (ndarray) Standard deviation of training input values, normalized.
Y (ndarray) Training model response values, normalized.
Y_mean (ndarray) Mean of training model response values, normalized.
Y_std (ndarray) Standard deviation of training model response values, normalized.
__init__(nugget=2.2204460492503131e-15, eval_rmse=False)[source]

Initialize all attributes.

Parameters:

nugget : double or ndarray, optional

Nugget smoothing parameter for smoothing noisy data. Represents the variance of the input values. If nugget is an ndarray, it must be of the same length as the number of training points. Default: 10. * Machine Epsilon

eval_rmse : bool

Flag indicating whether the Root Mean Squared Error (RMSE) should be computed. Set to False by default.

linearize(x)[source]

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

Parameters:

x : array-like

Point at which the surrogate Jacobian is evaluated.

Returns:

ndarray

Jacobian of surrogate output wrt inputs.

predict(x)[source]

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

Parameters:

x : array-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)[source]

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

Parameters:

x : array-like

Training input locations

y : array-like

Model responses at given inputs.

vectorized_predict(x)

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

Parameters:

x : array-like

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