Why are simple models often appropriate in industrial mathematics?

Abstract

The application of mathematical modelling has been spectacularly successful in understanding, controlling and improving industrial processes, despite the fact that many industrial processes are quite complex. Furthermore, many successful models used to describe them are relatively simple. We examine this apparent contradiction through a number of case studies where simple models have captured the essence of processes we have encountered in industry and elsewhere. A unifying feature is that industrial processes are often robust in the sense that they work effectively under a wide range of operating conditions. Often this is because key parts of the process tend to dominate. From a mathematical point of view, such processes are only weakly coupled to their environment, and a reductionist approach is often effective. In many cases, only a few key non-dimensional parameters associated with the underlying mathematical description dominate. Such problems are particularly amenable to simplifying mathematical analysis and approximation techniques.