Gaussian Process
The Gaussian Process function is intended for use with the Uncertainty Quantification Module, which is required for creating and training the Gaussian Process function. If you already have a model with a trained Gaussian Process function, that function can be evaluated without a license for the Uncertainty Quantification Module. It is also possible to copy and paste, or use the insert component functionality, for a trained Gaussian Process function from one model to another, without a license for the Uncertainty Quantification Module. For more information, see the Uncertainty Quantification User’s Guide.
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:
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Function names and argument names
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Function units and argument units
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Related functions settings
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Plot parameters
The Train Model functionality requires a license for the Uncertainty Quantification Module.
Model Settings
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.
Data
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.
Data Column Settings
Based on the content of the data source, a table is available with the following columns:
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 Columns: the names of the columns.
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 Type: choose one of the following types: Function name, Argument, or Ignored column depending on the content of the column.
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 Settings: In this column, the name of the function or argument appears. If the column type is set to Ignored column, the Settings column is empty.
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.
Training and Validation
In this section, you can specify a number of settings for the training and validation of the Gaussian process.
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.
Depending on choice of validation data, additional settings are available.
If you chose any other option than None:
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Specify a fraction of the validation data as a number between 0 and 1 in the Validation data fraction field (default: 0.1).
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Specify a table to use for the validation error using the Validation error table list. Choose New to create a new table.
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Specify a table to use for the validation predicted data using the Validation predicted data table list. Choose New to create a new table.
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.
Related Functions
In this section, you can define the following related function:
Standard Deviation Function
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.
Plot Parameters
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.