Background
Often when an engineer analyses a system or is supposed to control a system, he uses a mathematical model. In analysis, the engineer can build a descriptive model of the system as a hypothesis of how the system could work, or try to estimate how an unforseeable event could affect the system. Similarly, in control of a system the engineer can try out different control approaches in simulations.
A priori information
Mathematical modelling problems are often classified into white-box or black-box models, according to how much prior information is available of the system. A black-box model is a system of which there is no prior information available, and a white-box model is a system where all necessary information is available. Naturally, practically all systems are somewhere between the white-box and black-box models, so this concept only works as an intuitive guide for approach.
Complexity
Another basic issue is the complexity of a model. If we were, for example, modelling the flight of an airplane, we could embed each mechanical part of the airplane into our model and would thus acquire an almost white-box model of the system. However, the computational cost of adding such a huge amount of detail would effectively inhibit the usage of such a model. Additionally, the uncertainty would increase due to an overly complex system, because each separate part induces some amount of variance into the model. It is therefore usually apropiate to make some approximations to reduce the model to a sensible size. The engineer often can accept some approximations in order to get a more robust and simple model. For example Newton's classical mechanics is an approximated model of the real world. Still, Newton's model is quite sufficient for most ordinary-life situations, that is, as long as particle speeds are well below the speed of light, and we study macro-particles only.
See also: Applied mathematics, Neural networks
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