Mathematical models have been used in solving real-world problems from many
different disciplines. This requires building a suitable mathematical model. Two
different approaches to building mathematical models are as follows:
1. Theory-Based Modeling Here, the modeling is based on theories (from
physical, biological, and social sciences) relevant to the problem. This kind of
model is also called a physics-based model or white-box model.
2. Empirical Modeling Here the data available forms the basis for model
building, and it does not require an understanding of the underlying
mechanisms involved. This kind of model is also called as data-dependent
model or black-box model.