Model order reduction

Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling. Many modern mathematical models of real-life processes pose challenges when used in numerical simulations, due to complexity and large size (dimension). Model order reduction aims to lower the computational complexity of such problems, for example, in simulations of large-scale dynamical systems and control systems. By a reduction of the model's associated state space dimension or degrees of freedom, an approximation to the original model is computed which is commonly referred to as a reduced order model. Reduced order models are useful in settings where it is often unfeasible to perform numerical simulations using the complete full order model. This can be due to limitations in computational resources or the requirements of the simulations setting, for instance real-time simulation settings or many-query settings in which a large number of simulations needs to be performed. Examples of Real-time simulation settings include control systems in electronics and visualization of model results while examples for a many-query setting can include optimization problems and design exploration. In order to be applicable to real-world problems, often the requirements of a reduced order model are: A small approximation error compared to the full order model. Conservation of the properties and characteristics of the full order model (E.g. stability and passivity in electronics). Computationally efficient and robust reduced order modelling techniques. It is interesting to note that in some cases (e.g. constrained lumping of polynomial differential equations) it is possible to have a null approximation error, resulting in an exact model order reduction. Contemporary model order reduction techniques can be broadly classified into 5 classes: Proper orthogonal decomposition methods.
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