Model Reduction
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.
The creation of a reduced-order model can typically be divided into two steps: production of training data and model building. The resulting model can then be used for repeated simulations. When using the Modal method, the training data consists of solution vectors computed by some other study step or study steps. If these study steps are located in a different source study, then the Model Reduction study step assumes that the source study has been computed and that updated solution vectors can be found at the position corresponding to the training study step in an enabled solver configuration. When the training study steps are part of the same study sequence — that is, precede the Model Reduction step — the training data will be automatically recomputed each time the reduced-order model is rebuilt.
To add a Model Reduction node, first select Reduced-Order Modeling in the Show More Options dialog box.
There can only be one Model Reduction node in a study. When you copy a Model Reduction node, it is possible to paste it into another study without a Model Reduction node.
The following steps are the main steps needed to set up a model reduction study:
1
Select the model reduction method to apply: Modal (the default) or AWE.
2
For the Modal method only, select the training data. You must specify a study and study step providing eigenmodes. Constraint modes are not always needed but can be specified in the same way.
3
Select the unreduced (source) model (a study and study step reference).
4
Select to create or update an instance of the reduced model under Global Definitions>Reduced-Order Modeling.
5
For the Modal method only, specify if the reduced model should be capable of reconstruction.
6
For the Modal method only, define reduced-model control inputs under Model Control Inputs.
7
Define reduced-model outputs (similar to multiple objective functions). For the AWE method at least one of the outputs must be selected for use as quality indicator during the adaptive generation of the asymptotic waveform expansion.
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:
Model Reduction Settings
In this section, you specify how to run the model reduction.
Model-Reduction Method
From the Method list, choose one of the following model-reduction methods:
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The Modal method (the default) supports inputs and outputs and makes it possible to export ROM matrices.
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The AWE (asymptotic waveform evaluation) method is an alternative reduced-order model that provides a fast frequency sweep (an advanced interpolation) and supports outputs only.
Training Study (Modal Method Only)
From the Training study for eigenmodes list, choose an existing study for the eigenmode basis functions or choose None.
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 for the constraint basis functions or choose None (the default).
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).
Unreduced Model Study
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.
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 Child 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, select the Ensure reconstruction capability check box to enable reconstruction of the unreduced solution vector also when there are only linear outputs defined. For the AWE method, reconstruction is always enabled. The reduced-order model can then also assign reconstructed values to some of the dependent variables not solved for. This is controlled by the table with Reconstruction and Reduced-order model columns in the Physics and Variables Selection section in the destination study. 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.
For the Modal method, select the Store reduced matrices check box to store the reduced matrices from the model reduction in the solution data for exporting state-space matrices, for example.
The Use extra Compile Equations for Results check box 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 AWE method, enter a value for the Relative tolerance for adaptation (default: 0.01).
Model Control Inputs
In this section, you define the model control inputs when you use the Modal 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.
Outputs
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. If you do not add a name in the Variable column, the output is assigned a default variable name in the created reduced-order model.
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.
Results While Solving
This section is available for model reduction in the frequency domain only (AWE selected from the Method list).
See Results While Solving in the Common Study Step Settings section. Also see Getting Results While Solving.
Thermal Controller, Reduced-Order Model: Application Library path COMSOL_Multiphysics/Multiphysics/thermal_controller_rom.
If you have the Structural Mechanics Module, see Bracket — Reduced-Order Modeling: Application Library path Structural_Mechanics_Module/Tutorials/bracket_rom.