Figure 1. Overview of the role of mathematical modeling in the context of reactive systems.

The behavior of reactive systems can be described in mathematical terms that represent the underlying physical, kinetic, and reactive processes. The specific mathematical relationships incorporated into a model reflect a trade-off between computational and analytical tractability and realism that relate to the specific design objectives associated with how the mathematical model will be used. Modeling applications can be categorized into one of two applications. The first application, called forward modeling, predicts the behavior of the system based on prior knowledge of the relative importance of the physical, kinetic, and reactive processes. The second application is to identify aspects of reactive system that govern the behavior of the process using experimental observations of the system. This second application is called an inverse problem.