Use a Surrogate Model Training study node () to add functionality for training a surrogate model. A surrogate model is a simpler and computationally cheaper model, which you can use to approximate the behavior of a more complex and computationally expensive model (the full finite element model). In COMSOL apps, for example, faster model evaluation using the surrogate model provides users of the apps with a more interactive user experience. You create surrogate models by training a deep neural network (DNN), for example. The surrogate model training is typically based on output data from a large parametric sweep of the model for which you want to create a surrogate model. The training of a surrogate model needs a number of inputs and outputs, where the outputs are considered as functions of the inputs, which replace the full finite element solution. A large number of data points are needed in order to fully describe how the inputs map to the outputs. The outputs can be captured using domain point probes, for example.

A straightforward parametric sweep could densely and uniformly distribute input points, but such an approach would be inefficient. Random sampling is another alternative but with inherent drawbacks such as nonuniform sampling and potential failure to cover the entire input space. Instead, a more strategic approach is to use a design of experiments (DOE) method, carefully sampling within the parameter space. The Surrogate Model Training study uses Latin hypercube sampling (LHS), which is a DOE method that generates a dataset that uniformly covers the input space without requiring an excessive number of finite element computations. This property of LHS makes it an efficient method for data generation intended for the purpose of training a surrogate model.

For additional information about surrogate models in connection with uncertainty quantification, see the Uncertainty Quantification Module User’s Guide.

To add an Surrogate Model Training study, right-click a Study node and choose Surrogate Model Training. You can only have one Surrogate Model Training node in each study.

Click the Compute button () to initiate the surrogate model training and create a surrogate model.

If you choose Show Default Solver from the Study node, the Surrogate Model Training study generates and sets up a Design Of Experiments job and its subsequence node (see the Uncertainty Quantification Module User’s Guide). The Design Of Experiments job is controlled by and synchronized to the Surrogate Model Training study. If you click Compute from the Study node, the Surrogate Model Training study identifies and runs its Design Of Experiments job if it exists; else it first creates a Design Of Experiments job.

The Settings window for the Surrogate Model Training study include the following sections:

From the Compute actions list, choose one of the following options: Compute and build surrogate model (the default) or Improve and build surrogate model. Compute and build surrogate model will discard data from the previous run (if the same table is used) or start a new run using a new table. Improve and build surrogate model will add more data to an existing table, which can be useful if you realize after having examined the trained SM function that it does not seem accurate enough. The Surrogate Model Training study outputs training data tables and trained surrogate models for each quantity of interest. If you choose Design of experiments (No surrogate model) for the surrogate model in the Surrogate model list below, a training data table will be the only result.

From the Solution to use list, choose Automatic (the default), Summation, Minimum, Maximum, Use first, or Use last. The Automatic solution to use will be the last solution for time-dependent and parametric solutions, while for eigenvalue and eigenfrequency solutions, it will be the first solution. You can override this mechanism by selecting any of the other methods. For Summation, the quantity of interest (QoI) is defined as the summation of the Expression over all the solutions. For Maximum (or Minimum), the QoI is defined as the maximum (or minimum) of the expression taken over all the solutions. Also note that evaluation operators like at() and with() can be used in the expression, making it possible to evaluate even more general quantities from dynamic solutions.

From the Surrogate model list, choose None (Design of Experiments) (the default) to use a DOE model, or choose Gaussian process, Polynomial chaos expansion, or Deep neural network: Gaussian process and Polynomial chaos expansion require a license for the Uncertainty Quantification Module.

In the table under Quantities of interest (Outputs), define the outputs from the surrogate model (quantities of interest), which could be defined as point probe expressions, for example.

In the Expression column, type the expression for the output (comp1.ppb1, for example, for a Point Probe Expression 1 in Component 1). In the Description column, type a description for the output (Temperature, for example). In the Individual solution to use column, the default is From "Solution to use" to use the solution specified in the Solution to use list above. You can also choose Automatic, Summation, Minimum, Maximum, Use first, or Use last. Use the Move Up (), Move Down (), and Delete () buttons and the fields under tables to edit the table contents. Or right-click a table cell and select Move Up, Move Down, or Delete. The Add button () adds a new output to the list. Use the Clear Table button () to clear the entire table.

For the input parameters, in the Parameters column, choose the parameter from a list of all global parameters in the model. In Source type column, choose Analytic (the default) or Data.

If you chose Analytic, you can define the following properties for the selected parameter underneath the table:

The chosen analytic distribution appears in the Parameter description column.

If you chose Data in the Source type column, you can instead specify the following properties:

If the source type for the parameter is Analytic, you can add correlations groups. Doing so allows sampling of parameters that are not statistically independent by specifying a correlation matrix. You could select a subset of all input parameters in the same correlation group, and set the correlation matrix to specify the correlation between each pair of two parameters. Multiple correlation groups can be added in one study, and one parameter can only appears in one correlation group. The correlation matrix is a symmetric semidefinite matrix where all the diagonal elements equal to 1 and all the off-diagonal elements are between [−1, 1].

Under Input parameters sampling settings, specify the following setting if the source type is Analytic:

Select the Accumulated probe table check box to add accumulated probe tables for the result from the surrogate model training. From the Output table list, choose New to create a new table, or choose any existing table. The Use all probes check box is selected by default to accumulate all the model probes in the table. If you clear this check box, the probes selected from the Probes list are used.

From the Error handling list, choose Stop immediately (the default) or Skip problematic parameters.

From the Keep model evaluations in memory list, choose Only last (the default) to only keep the last model evaluation in memory, or choose All to keep all model evaluations.

From the Default solver sequence generation list choose Using global parameters (the default) or Using each parameter tuple. Use this setting to control whether a solver sequence should be generated using global parameters or each parameter tuple.

Select the Reuse the solution from the previous step check box if you want the surrogate model training algorithm to reuse the solution from the previous step. It is useful if you are using an iterative solver and the solutions for different parameter values are similar enough so that it is faster to start from the previous solution instead of starting the solver from scratch.

Select the Distribute model evaluation check box if you are running the COMSOL software on a multiprocessor system and want to distribute the model evaluation to each compute node for improved performance.

From the Surrogate model training log list, choose Minimal, Normal (the default), or Detailed as desired.