The tremendous advances in numerical analysis as well as in computing power in the past decades have resulted in the availability of computational methods for increasingly complex systems. These systems typically involve a variety of parameters (e.g. physical, geometric, loading, or control parameters), possibly affected by uncertainties. Furthermore, in many applications, the goal is not to merely predict the system behavior, but to solve an inverse, design, control, optimization, parameter estimation problem, possibly in real-time and possibly taking into account uncertainties.
The solution of such problems typically requires repeated simulations at many different parameter values. For complex systems, this task can easily become infeasible despite increased computing capabilities. Thus, fast and reliable reduced computational models are needed. Model reduction has been a very active area of research for the past decades.