Many modern mathematical models of real-life processes pose challenges when used in numerical simulations, due to complexity and large size (dimension).
[5] Contemporary model order reduction techniques can be broadly classified into 5 classes:[1][6] The simplified physics approach can be described to be analogous to the traditional mathematical modelling approach, in which a less complex description of a system is constructed based on assumptions and simplifications using physical insight or otherwise derived information.
However, this approach is not often the topic of discussion in the context of model order reduction as it is a general method in science, engineering, and mathematics.
Computational fluid dynamics studies often involve models solving the Navier–Stokes equations with a number of degrees of freedom in the order of magnitude upwards of
The first usage of model order reduction techniques dates back to the work of Lumley in 1967,[28] where it was used to gain insight into the mechanisms and intensity of turbulence and large coherent structures present in fluid flow problems.