12 Facts About Mathematical models

Mathematical models are used in the natural sciences and engineering disciplines, as well as in non-physical systems such as the social sciences.

The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research.

Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models.

In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments.

Therefore, the white-box Mathematical models are usually considered easier, because if you have used the information correctly, then the model will behave correctly.

In black-box Mathematical models, one tries to estimate both the functional form of relations between variables and the numerical parameters in those functions.

An often used approach for black-box Mathematical models are neural networks which usually do not make assumptions about incoming data.

The advantage of NARMAX Mathematical models compared to neural networks is that NARMAX produces Mathematical models that can be written down and related to the underlying process, whereas neural networks produce an approximation that is opaque.

Statistical Mathematical models are prone to overfitting which means that a model is fitted to data too much and it has lost its ability to generalize to new events that were not observed before.

Mathematical models are of great importance in the natural sciences, particularly in physics.

For example, molecules can be modeled by molecular orbital Mathematical models that are approximate solutions to the Schrodinger equation.

In engineering, physics models are often made by mathematical methods such as finite element analysis.