Mechanistic models serve as variable prediction tools, particularly when substantial knowledge about a process with well-defined characteristics is available. These models are constructed typically using sets of differential equations, a practice known as 'mechanistic' model development, which draws from the fundamental principles of physics and chemistry governing the process. When a mechanistic model of a system is available and accurately represents the system's behavior, it can be incorporated directly into a MPC framework. In this case, the mechanistic model serves as the predictive model used by MPC. For instance, in wastewater treatment, mechanistic models are crafted by formulating the biochemical and physical processes within the reactor, yielding calibrated kinetic and stoichiometric parameters that explain observed outcomes and enhance process understanding. Mechanistic models, often expressed as systems of ordinary or partial differential equations, offer advantages such as robust process representation and superior extrapolation capabilities compared to data-driven models. Often calibration of parameters is needed, and therefore more data needs to be collected, in order to keep the model able to describe the reality.
(Source: Between the Poles of Data-Driven and Mechanistic Modeling for Process Operation & A review of mechanistic and data-driven models of aerobic granular sludge)