Reduced-Order Model Inputs

There are two types of possible inputs to a reduced-order model: on one hand, fundamental parameters like the time (t) in a transient model and the frequency (freq) in a frequency-domain model, and, on the other hand, general parameter names that can be used to modify expressions and equations. Model reduction methods differ as to which fundamental parameters they can handle, as well as if and how they allow general parameters to be used.

During the training phase, the model reduction process must be able to evaluate the dependency of outputs on inputs. For fundamental parameters, this is built into the equation formulation itself. But general dependency evaluations can only be performed with respect to degrees of freedom in the model. Therefore, any quantity that you want to use as a general input parameter to a reduced-order model must be temporarily redefined as a degree of freedom during the training phase. And it must then also evaluate to a constant training value, independent of time, frequency or other inputs.

At the same time, a general input parameter must behave like a normal user-defined variable when the full, unreduced, model study is computed or when it is used explicitly in a calling model. For example, it can be time- or frequency-dependent in that situation.

Reduced-order model inputs are special variables that have these desired properties: they are defined by an expression during normal computations, where they can be used exactly like any other user-defined variable. But they are internally redefined as degrees of freedom when necessary for training a Reduced-Order Model. The Model Reduction study step (see Model Reduction) allows only such predefined reduced-order model inputs as inputs to the training process.

For example, consider an input parameter f representing a time-varying force on a model. In the full, unreduced model, it is defined as some function of time f(t) that will be used if you compute a time-dependent study. This is good practice as a way to check correctness of the unreduced model. When you add a Model Reduction study to the full model in order to train a reduced-order model, it will have to linearize the behavior around some nominal value f0. To do that, the Model Reduction study step will temporarily turn f in to a degree of freedom, with respect to which it can compute sensitivities. And it will initialize that degree of freedom to f0.

In the reduced-order model created by the Model Reduction study step, you can specify the actual expression that will be used as input values when calling the online model. This can be any expression, say g(t), that can be evaluated in the calling model, but it is by default set to equal the original input name in the unreduced model. When the calling model is the same as the unreduced model, which is the most common situation, this means that the force input to the reduced-order model in this example evaluates to f(t), like in the unreduced model.