Empirical Modeling
Empirical models have a generic and flexible model form that can fit many physical phenomena without a fundamental understanding of the process. This allows a non-process expert to derive a predictive model for simulation, estimation, or control. Empirical models are often numerically less expensive to solve and train. While increasing the number of model parameters leads to a better fit of the data, there is often poor extrapolation outside of the training region.
Fundamental Modeling
Fundamental modeling of many physical systems can be described with differential and algebraic equations (DAEs). When used in predictive analytics, these models can have a much wider range of accuracy than empirical models. Although sometimes difficult to construct, parts of a fundamental model can be reused in similar applications. The ability to re-use fundamental models is because the underlying model structure is based on fundamentals that do not change from application to application.