The ambiguity of the term "model," the enormous number of modeling types, and their rapid development currently make it difficult to construct a logically complete classification of models that would satisfy everyone. Any such classification is conventional, since it reflects, on one hand, the subjective viewpoint of its authors, and on the other, the limits of their knowledge across a finite number of domains of scientific inquiry.
The classification presented here should be viewed as an attempt to construct a tool — or a model — for investigating the properties and characteristics of the modeling process itself. Modeling is a general scientific method of inquiry. The use of modeling at both the empirical and theoretical levels of research leads to a conventional distinction between physical (material) and abstract (ideal) models.
Physical modeling is the investigation of an object using a material analog that reproduces its principal physical, geometric, dynamic, and functional characteristics. The main types of physical modeling are full-scale (prototype) modeling and analog modeling. Both types are based on the properties of geometric or physical similarity.
Abstract modeling differs from physical modeling in that it is based not on a materialized analogy between the object and the model, but on an ideal, conceptual analogy, and is always theoretical in character. Abstract modeling is primary with respect to physical modeling: first, an ideal model forms in the human mind, and only then is a physical model built on its basis.
The main types of physical modeling are full-scale and analog. Both are based on the properties of geometric or physical similarity. Two geometric figures are similar if the ratios of all corresponding lengths and angles are the same. If the similarity coefficient — the scale — is known, then the dimensions of one figure can be multiplied by the scale factor to determine the dimensions of the other, geometrically similar figure. Two physical phenomena are similar if, given the known characteristics of one, the characteristics of the other can be obtained by a simple conversion analogous to transitioning from one system of measurement units to another. The study of the conditions of similarity between phenomena is the domain of similarity theory.
Full-scale modeling is modeling in which a real object is represented by an enlarged or reduced material analog that lends itself to investigation (typically under laboratory conditions), with the subsequent transfer of the properties of the studied processes and phenomena from the model to the object based on similarity theory.
Analog modeling is modeling based on the analogy between processes and phenomena that have different physical natures but are described formally in the same way (by the same mathematical relations, logical diagrams, and structural schemes). Analog modeling rests on the coincidence of the mathematical descriptions of different objects.
Physical and analog models are material reflections of a real object and are closely linked to it through their geometric, physical, and other characteristics. In practice, investigating models of this type amounts to conducting a series of physical experiments in which the real object is replaced by its physical or analog model.
Abstract modeling is divided into two main types: intuitive and scientific.
Intuitive modeling is modeling based on an intuitive (not justified from the standpoint of formal logic) conception of the object under study — one that does not lend itself to formalization or does not require it. The most vivid example of an intuitive model of the surrounding world is a person's life experience. Any empirical knowledge that lacks an explanation of the causes and mechanisms of the observed phenomenon should also be considered intuitive.
Scientific modeling is always logically grounded, using a minimum number of assumptions adopted as hypotheses on the basis of observations of the object being modeled.
The key difference between scientific and intuitive modeling lies not only in the ability to perform the necessary operations and actions involved in modeling, but also in understanding the "internal" mechanisms employed. One can say that scientific modeling knows not only how to model but also why it should be done in a particular way. It must be emphasized that intuition and intuitive models play an extraordinarily important role in science — no genuinely new knowledge can be attained without them. Such knowledge is unattainable by the methods of formal logic alone.
Intuitive and scientific (theoretical) modeling should in no way be set in opposition to one another. They complement each other well, each occupying its own domain of application.
Symbolic modeling is modeling that uses sign-based representations, such as diagrams, graphs, drawings, and sets of symbols, together with the laws and rules governing their manipulation. Examples of such models include any language — for instance, the language of spoken and written human communication, algorithmic languages, and so on. The symbolic form is used to convey both scientific and intuitive knowledge. Modeling by means of mathematical relations is also an example of symbolic modeling.
Intuitive knowledge is a generator of new knowledge. However, far from all conjectures and ideas withstand subsequent verification by experiment and by the methods of formal logic characteristic of the scientific approach, which serves as a kind of filter for identifying the most valuable knowledge.