What is Model order Reduction

From Model order reduction site at MIT

Model Order Reduction (MOR) is a branch of systems and control theory, which studies properties of dynamical systems in application for reducing their complexity, while preserving (to the possible extent) their input-output behavior.

This problem applies both to continuous-time and discrete-time systems.

Let's assume that you have some device and you have obtained (say, using finite-difference discretization or other techniques) its description in the form of a differential equation. Usually you will get a system of a very high order, evidently redundant for representing some properties you are interested in. How can we create a possibly smallest model while preserving system's behavior - this is the topic of MOR.

For example, consider transmission line. We can obtain its dynamical model by discretizing its length, representing each small piece as a small resistor, inductor plus capacitor to the ground, then create a description using nodal voltage analysis; and by solving this system for any given input we will know a voltage distribution at any given point of the line. Now assume that we are not interested in knowing the exact distribution of a voltage along the line, but we are interested in how the signal is transmitted through the line - i.e. we need to know the dependence of voltage and current at the one end of the line on the voltage and current at another end of the line. In order to simulate this line efficiently (especially if this line is part of some complex circuit!), you need a "simplified" representation of this line. Model order reduction process will produce this small approximation for you.

Goals and problems of the model order reduction

• To make a reduction process automatic (the algorithm doesn't know anything about the nature of underlying system)
• Sometimes we need to preserve some system properties, such as passivity, stability, etc.
• To ensure good approximation of the original system by the reduced system in various aspects
• Maybe we may vary some parameter of a system (i.e. length of transmission line). We need to be able to create parametrized reduced models.
• Since non-reduced models may have millions of unknowns, the algorithm must be efficient.

Some of these problems are well-developed for some cases (especially for linear systems),
but most of these problems (especially for nonlinear systems) are still heavily under development.