As is used in connection with systems engineering, a model is a qualitative or quantitative representation of a process or endeavor that shows the effects of those factors which are significant for the purposes being considered. Modeling is the process of making a model. Although the model may not represent the actual phenomenon in all respects, it does describe the essential inputs, outputs, and internal characteristics, as well as provide an indication of environmental conditions similar to those of actual equipment.

A model may be pictorial, descriptive, qualitative, or generally approximate in nature, or it may be mathematical and quantitative in nature and reasonably precise.

The word model is used as a noun, adjective, and verb, and in each instance it has a slightly different connotation. As a noun "model" is a representation in the sense in which an architect constructs a small-scale model of a building or a physicist a large-scale model of an atom. As an adjective "model" implies a degree or perfection or idealization, as in reference to a model home, a model student, or a model husband. As a verb "to model" means to demonstrate, to reveal, to show what a thing is like.

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work - that is correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple.

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.

First of all I want to remind you of the essential features of models. In my opinion they are: (i) drawing up a list of the variables to be considered; (ii) drawing up a list of the equations or relations the variables have to obey and (iii) testing the validity of the equations, which implies the estimation of their coefficients, if any. As a consequence of especially (iii) we may have to revise (i) and (ii) so as to arrive at a satisfactory degree of realism of the theory embodied in the model. Then, the model may be used for various purposes, that is, for the solution of various problems. The advantages of models are, on one hand, that they force us to present a "complete" theory by which I mean a theory taking into account all relevant phenomena and relations and, on the other hand, the confrontation with observation, that is, reality. Of course these remarks are far from new.

We build models to increase productivity, under the justified assumption that it's cheaper to manipulate the model than the real thing. Models then enable cheaper exploration and reasoning about some universe of discourse . One important application of models is to understand a real, abstract, or hypothetical problem domain that a computer system will reflect. This is done by abstraction, classification, and generalization of subject-matter entities into an appropriate set of classes and their behavior.

For the scientist a model is also a way in which the human though processes can be amplified. This method often takes the form of models that can be programmed into computers. At no point, however, the scientist intend to loose control of the situation because off the computer does some of his thinking for him. The scientist controls the basic assumptions and the computer only derives some of the more complicated implications.

Models are used essentially for evaluation and prediction purposes as well as for the analysis and study of the different parts of the system so that the systems engineer or designer may arrive at sound engineering decisions regarding the system design.

Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns.

Model building is the art of selecting those aspects of a process that are relevant to the question being asked. As with any art, this selection is guided by taste, elegance, and metaphor; it is a matter of induction, rather than deduction. High science depends on this art.

Scientific models have all these connotations. They are representations of states, objects, and events. They are idealized in the sense that they are less complicated than reality and hence easier to use for research purposes. These models are easier to manipulate and "carry" than the real thing. The simplicity of models, compared with reality, lies in the fact that only the relevant properties of reality are represented.

Modeling Principle: Models are not right or wrong; they are more or less useful.

mental model is simply a representation of how something works.