Reduced-Order Modeling

A Reduced-Order Model is a feature in a COMSOL Multiphysics model that encapsulates important aspects of the behavior of another model in a computationally efficient form. From the perspective of a COMSOL Multiphysics model that uses a reduced-order model, it is essentially a black box with a well-defined interface. Depending on the type of reduced-order model, it can, in addition to inputs and outputs, interact with the surrounding model via reduced-order equations, internal states or matrix representations of the model.

A reduced-order model must be trained so as to reproduce the behavior of a full, unreduced, COMSOL Multiphysics model and study step. The training of a reduced-order model is sometimes referred to as the offline phase, and its subsequent use as the online phase. Reduced-order models are normally created and trained by a study step (see Model Reduction) but some types can also be imported from a COMSOL Reduced-Order Model file (*.mphrom).

Outputs from a reduced-order model are made available to the model where it is used (the caller) in the form of variables or operators. These can be used as parts of expressions and equations when computing the calling model as well as in postprocessing.

The interface through which a calling model interacts with a reduced-order model in COMSOL Multiphysics belongs to one of two fundamental types: it is either stateless or stateful. A reduced-order model with a stateless interface is a black box with a number of inputs and a number of outputs. The reduced-order model may have internal states which are solved by an internal solver, but these are not exposed to the solver used for solving the calling model. Because a reduced-order model with a stateless interface uses its own internal solver, it can be passed new input values and generate new results directly in postprocessing, without having to run a main solver.

A reduced-order model with a stateful interface, in contrast, relies on the main COMSOL solvers to solve a set of reduced-order equations in terms of states (degrees of freedom) which are exposed to the main solver and subsequently stored in the main solution vector. In this respect, a stateful reduced-order model behaves similarly to a physics interface. Output values can only be computed for the values of the reduced-order model’s inputs at the time the main solver was run. It is not possible to change inputs in postprocessing to generate new outputs.

A reduced-order model can, for example, be used for:

When a model contains a reduced-order model, it is represented as a node under the node (

) under . See the following sections for information about the available reduced-order model types, concepts, and associated modeling tools: