The Gaussian Process function () defines a Gaussian process, which is a popular surrogate model that gives an approximate prediction of the quantities of interest in an uncertainty quantification analysis, is probabilistic, and computes the variance of the prediction at every sample point in the input parameter space. The default Function name is gpm1.

Click the Train Model button ()) to compute internal data that is needed before the function can be evaluated. For most changes made in this Settings window, the function needs to be trained again for the changes to take effect. The following settings take effect immediately without retraining:

The Train Model functionality requires a license for the Uncertainty Quantification Module.

Define the covariance for the Gaussian process using the Covariance list. Choose Squared exponential, Matérn 3/2 (the default), Matérn 5/2, or Single-layer neural network. See Surrogate Models — Gaussian Process in the Uncertainty Quantification User’s Guide for more information.

From the Mean list, choose Constant (the default), Linear, or Quadratic for the mean function in the Gaussian process.

Select a Data source — File or Result table to define the data source for the Gaussian process.

If you select File (the default), enter the complete network path and name of the data file in the Filename field, or click Browse to select a text or data file with data in the Interpolation Data dialog box. You can import data files with comma-separated, semicolon-separated, space-separated, and tab-separated data. You can also click the downward arrow beside the Browse button and choose Browse From () to open the fullscreen Select File window. Click the downward arrow for the Location menu () to choose Show in Auxiliary Data () to move to the row for this file in the Auxiliary Data window, Copy Location (), and (if you have copied a file location) Paste Location (). Also choose a decimal separator from the Decimal separator list: Point (the default) or Comma. Click Import () to import the data into the model; otherwise, COMSOL Multiphysics references the data on your file system. Click Export to save the data for the Gaussian process to a file and reference from there instead of including it in the model. Click the Discard button to delete the imported data for the Gaussian process from the model. Click the Refresh button ()to ensure that the file is reread when needed.

If you select Result table, choose the table to use from the Result table list.

When selecting a row in the Settings column, you can edit the name of the function or argument in the Name field underneath and also provide a unit in the Unit field.

From the Method for number of restart points list, choose Automatic (the default) or Manual. If you chose Manual, you can specify the Number of restart points (default: 10). If you chose Automatic, the software reports the Number of restart points for training.

In the Maximum matrix size field, specify the largest matrix size (default: 2000). The matrix size is equal to the number of rows in the input data.

From the Random seed type list, choose Fixed (the default) or Current computer time. If you chose Fixed, you can specify a seed in the Random seed field.

Under Post-training test data, choose an option from the Validation data list: None, Random sample of data values, Every N:th data value, Last part of data value, or Separate table.

If you chose any other option than None:

If you chose Random sample of data values, also specify a Random seed (see above).

If you chose Separate table, a Validation data table list is available, and the Validation data fraction setting is not available.

To define a function for the standard deviation, select the Define standard deviation function check box and enter a suffix for the standard deviation function in the Function name suffix field (the default is _stddev). The suffix is added to the names of the main functions, which are defined in the Data Column Settings section. For example, if you have defined two function type columns with corresponding names gpm1_a and gpm1_b, the names of the related standard deviation functions will be gpm1_a_stddev and gpm1_b_stddev, respectively, if the function name suffix is _stddev.

From the Function name list, choose the function values to plot.

Use the table below to set the range for arguments in preview plots. For each argument, enter a Lower limit, and an Upper limit in the Plot Parameters table. Use the check boxes in the Plot column to control which arguments to use in the plot (you can select a maximum of three arguments). If you clear a check box, a constant value, taken from the argument’s lower limit, is used. Constant arguments do no use an axis in the plot. These values and settings are used when you click the Plot button () or the Create Plot button () at the top of the Settings window.