Use a Model Reduction study node () to create a reduced-order model (ROM) based on a time-dependent or frequency-domain simulation (see Reduced-Order Modeling). Reduced-order models are usually thought of as computationally inexpensive mathematical representations that provide the ability to run faster simulations using a small model that captures the dynamic behavior of the original model.

Click the Compute button () (or press F8) at the top of the Settings window to produce an instance of the reduced-order model under Global Definitions > Reduced-Order Modeling.

The Settings window contains the following sections:

From the Method list, choose one of the following model-reduction methods:

From the Unreduced model study list, choose a study that contains at least one study step of a type that can be reduced using the selected model-reduction method, or the parent study of the current Model Reduction node. When another study is selected, select an applicable study step from the Defined by study step list. When you have chosen POD, also specify a specific solution to use from the Solution selection list.

From the Training study for eigenmodes list, choose an existing study whose solution can be used as eigenmodes. If you choose None, no eigenmode is selected. The solution from any eigenvalue type of study can be used as eigenmodes.

From the Study step for eigenmodes list, choose Automatic (the default) to use the last applicable solution in the solver sequence, or select any of the applicable study steps (such as Eigenvalue).

From the Training study for constraint modes list, choose an existing study whose solution can be used as constraint modes. If you choose None (the default), no constraint mode is selected.

From the Study step for constraint modes list, choose Automatic (the default) to use the last applicable solution in the solver sequence, or select any of the applicable study steps (such as Stationary).

Constraint modes are introduced mainly to handle the constraints that are controlled by inputs in the Global Reduced-Model Inputs node in the unreduced problem. There are two different ways to generate the constraint modes. One is via Auxiliary sweep settings in the Study Extensions section of a Stationary study step. First, define the same number of training parameters as the number of inputs that are used by constraints like Dirichlet boundary conditions in the unreduced problem. Training parameters are defined under Global Definitions > Parameters. Then, for each Dirichlet boundary condition defined by the inputs, define another Dirichlet boundary condition using the training parameter and enable those training boundary conditions in the stationary study. Last, in the auxiliary sweep of the stationary study, set one training parameter to be 1 at a time and set all other training parameters to be zero. The resulting parametric solutions can be used as constraint modes candidates. The other method is via a sensitivity solution. For this method, defining training parameters and training boundary conditions are not needed. Rather, you create a Sensitivity interface on top of the stationary study step and then add the control input in the Parameter name column in the Control Variables and Parameters table in the Sensitivity interface. The generated sensitivity solution with respect to each control variable can be used as a candidate for constraint modes.

If the parent study is selected, the unreduced model study step is expected to be a subnode to the Model Reduction node. Right-click the Model Reduction node and add either a Frequency Domain or a Time Dependent study step from its context menu. Then select it from the Defined by study step list.

From the Reduced-order model list, choose New to create a new reduced-order model, or choose any existing and compatible reduced-order model (available under Global Definitions > Reduced-Order Modeling).

If the model-reduction method is Modal or POD, the Ensure reconstruction capability checkbox is selected by default to enable reconstruction of the unreduced solution vector also when there are only linear outputs defined. Clear it if you need to save memory; for the ROM to be capable of reconstruction, the modal basis must be stored.

During the online use case, the reduced-order model can then assign reconstructed values to some of the dependent variables not solved for. To do so, go to the Physics and Variables Selection section in the destination study that uses a reduced-order model. If the Modify model configuration for study step checkbox is not selected, there is a table with Reconstruction and Reduced-order model columns. There is a row for each physics interface that is not solved whose dependent variables can be reconstructed by at least one reduced-order model. The Reconstruction column shows the physics interface name. The list in the Reduced-order model column determines which reduced-order model (if any) should be asked to reconstruct the fields for this physics interface. If the Modify model configuration for study step checkbox is selected, there is no such table; instead, there is a Reconstruction field where you can choose the reduced-order model.

The Use extra Compile Equations for Results checkbox is selected by default. This setting controls whether an extra, active Compile Equations node will be added last in the default solver sequence. The extra Compile Equations step is equivalent to an Update Solution call for the unreduced model study step. Most importantly, it includes the newly created reduced-order model feature in the final solution output by the study so that the reduced-order model’s outputs can be evaluated directly using this solution. The extra Compile Equation node is not necessary when the reduced-order model will only be called from some other study. In particular, when multiple reduced-order models are created in a sweep, it can be removed to save computation time.

For the POD method, the value in the Relative tolerance for truncations field is used to determine the number of POD modes so that the relative error of approximating a training solution with POD modes is within the specified threshold (default value: 0.01).

In this section, you define the model control inputs when you use the Modal method or POD method. The Model Control Inputs table consists of three columns: Reduced-model input, Use, and Training expression. The Reduced-model input column shows all the variables defined in the Global Reduced-Model Inputs node under Global Definitions. When the variable is added to the Global Reduced-Model Inputs it is automatically added to the Model Control Inputs table. The Use column controls which of the defined variables that should be used. In the Training expression column, enter a training expression around which the model reduction will linearize the model. Note that the training expression value is not passed on to the training study steps: if their solution depends on reduced-order model input variables, they have to be recomputed manually when changing the training value. Also note that it is important to give the training expression (possibly time dependent) whose initial values and initial time derivatives are consistent with the usage of the inputs in constraints (in its online form).

After running the Model Reduction study, those control inputs show up in the Model Control Inputs table in the generated reduced-order model node.

In the Outputs section, add outputs for the reduced-order model. You can add output variables by clicking the Add Expression () and Replace Expression () buttons to search through a list of predefined expressions. The Outputs table consists of three columns: Variable, Expression, and Description. The Variable column defines all output variable names. The Expression column provides definitions for the variables. The Description column contains descriptions for the variables. After running the Model Reduction study, those output variables show up in the Outputs section in the generated reduced-order model node.

This method has some settings common with the Modal method. The common settings include the following: Unreduced model study, Defined by study step, Training study for constraint modes, Study step for constraint modes, Reduced-order model, Ensure reconstruction capability, and Use extra Compile Equations for Results. See Settings for the Modal Method for a detailed explanation.

From the Solution selection list, choose a solution for POD modes training.

The value for Relative tolerance for truncations is used to determine the number of POD modes so that the relative error of approximating a training solution with POD modes is within the specified threshold.

For the Model Control Inputs and Output section, also see Settings for the Modal Method.

This method has some settings in common with the Modal method. The common settings include the following: Unreduced model study, Defined by study step, Reduced-order model, and Use extra Compile Equations for Results. See Settings for the Modal Method for a detailed explanation.

For the AWE method, reconstruction is always enabled. See the information about the Ensure reconstruction capability checkbox in Settings for the Modal Method for how reconstruction works.

For the AWE method, enter a value for the Relative tolerance for adaptation (default: 0.01) see the documentation for the relative tolerance in the AWE Solver.

The AWE method uses the output expressions to measure expansion accuracy during the adaptive training process. The expansion is refined until each output expression evaluates to the same value (to the specified tolerance) when computed using the left and right expansions at a number of sampling points in each interval. Clear the Use for adaptation column to exclude an output from the adaptation error control. Use the Scale column to indicate what is a typical value of the output. An adaptation error below 0.001 times the scale is by default considered to be acceptable. This absolute tolerance can also be changed in the AWE Solver settings.