# The “Metamodel” tab¶

At this tab you will use the Design of Experiments (DOE) generated previously to generate kriging metamodels of the initial sampling. The main idea here is to inspect if the initial sampling providing is capable of predicting the basic form of the functions that you chose/created on the first step (Objective Function, CV candidates and constraints). If the kriging generated by the initial sampling is good enough, you are able to optimize it and refine it on the next step. On this tab you will be able to:

Define the lower and upper bounds for the hyperparameters that will be adjusted to give the best kriging prediction

Define the regression and correlation (kernel) model for your kriging interpolator

Define which variables will have their kriging metamodel built

Inspect several validation metrics in order to conclude if your model is a good representation

Perform k-fold or hold-out validation. On the latter, you will be able to also inspect graphically your model.

Here is an overview of this tab:

There are six main panels on this tab:

Hyperparameters (theta) definition

*panel*Regression and Correlation (Kernel) model selection

*panel*Type of validation

*panel*Variable selection

*panel*Results generation and validation

*panel*Validation metrics

*panel*

## Hyperparameters (theta) definition *panel*¶

This is the panel that you will define the upper and lower bounds of the Hyperparameters (theta). There is one hyperparameter for each MV. The disturbances are only included at the “Reduced space” step, since we seek to use the first metamodel to optimize the base case.

Important

Generally, you do not need to change from the
defaults values used in *Metacontrol*, since internally *PyDACE* does a pretty good job in optimizing the
Hyperparameters to maximize the likelihood. We recommend to change the bounds or even the
estimate only if you are not satisfied with the prediction produced. For the mathematical aspects and a deeper
explanation on how the hyperparameters (and kriging itself) works, check our “Theoretical Backgrounds” Section.

### Changing the bounds and estimate for the hyperparameters¶

Simply double click on the upper/lower bound/estimate that you want to change and type it. Easy.

## Regression and Correlation (Kernel) model selection *panel*¶

This panel is used to configure which regression and correlation (kernel) model will be used in your kriging interpolator.

### Selecting the regression and correlation models¶

Just use the dropdown list to select the regression and correlation models.

Important

Currently, *Metacontrol* gives you the *constant*, *linear* and *quadratic* options for
the regression model, and the *exponential* for the kernel. On future releases, different kernels
will be added.

## Type of validation *panel*¶

This panel will give you the possibility to opt between *hold-out* (leave-out) or *k-fold* types of validation.
The number of folds and the percentage of DOE data separated for the training set in the case of *hold-out* validation
can also be configured.

### Performing a *hold-out* Validation¶

Select the radio button for *hold-out* validation and define using the slider the percentage of the initial sampling
that is going to be used to build your model. The remaining will be used for test purposes.

The *Metacontrol* default is to leave 75% of the DOE data for construction and the remaining for
validation purposes.

### Performing a *k-out* Validation¶

Select the radio button for *k-fold* validation and define the number of folds to be considered using the slider.

Important

For a theoretical background on *hold-out* and *k-fold* validation, refer to our papers and our theoretical
background section.

## Variable selection *panel*¶

On this panel you can choose which variables will have their model built. *Metacontrol* gives you this feature
in order to give you the chance to inspect groups of variables, for instance.

### Selecting a variable to have its model built¶

Simply check the box for each Variable (Objective Function, CV candidate, constraint function) That you want to inspect its kriging response:

## Results generation and validation *panel*¶

After configuring the hyperparameters bounds/estimates, choosing your kernel and regression models, selecting which variables do you want to have kriging responses generated and the type of validation, you can use this panel to generate your kriging responses.

If you choose *k-fold* validation, you will see that the Validation metrics *panel* is now with several metrics to evaluate your kriging model.

If you choose *hold-out* validation, you will see that, in addition to the results of the Validation metrics *panel*, the button “View graphical results”
is available.

### Graphically inspecting your results¶

The classic predicted data *versus* validation data validation plots are available in *Metacontrol*, if you opted for *hold-out* validation. Simply click on
“View graphical results” button, and a screen with a plot for each variable that had its kriging response built will appear:

Taking a closer look to the “Validation Results” windows with the plots you can see a panel at the bottom with several buttons. They allow you to:

Reset the original view, if you change it

Pan axes with left mouse, zoom with right

Zoom to rectangle

Configure subplots

Edit axis, curve and image parameters

Save the figure to use it elewhere.

## Validation metrics *panel*¶

This panel is completed after you generate your kriging metamodel. It allows you to see several metrics in order to assure the robustness of you kriging response.

The metrics are:

OMSE = Overall Mean-squared Error

ORMSE = Overall Root Mean-squared Error

OMAE = Overall Mean Absolute Error

OR2 = R² value

OEV = Overall expected Variance

Sample Mean

Sample Standard deviation