Simulation Systems Department.

In the discourse below "mathematical model" is treated as the set of equations (more generally the set of relations) between the characteristics of some phenomena (processes, systems). The unknown characteristics of mathematical models in terms of which the predictions are formulated and which are intended to reveal the means of mathematical modeling are called 'endogenous' (or prognosis, or inner, or phase variables) characteristics. The 'exogenous' (or outer, or parameters) characteristics are also used in many mathematical models. The endogenous characteristics of mathematical models are significantly influenced by their exogenous characteristics, while from the practical point of view (i.e. considering some conditions within the framework of certain correctness) opposite influence does not take place. Mathematical models (i.e. the set of relations) will be called there 'closed', if its endogenous characteristics may be defined by the set of relations as soon as its exogenous characteristics are known. Thus 'hypothesis about independence' presents the basis of any closed (and therefore capable to make prognosis) mathematical model. The essence of hypothesis about independence is presented here: one system of characteristics of phenomena (process, system) depend significantly on other system of characteristics but opposite dependence is absent with practical point of view. Several fundamental principles of independence, which usually are called 'lows' often serve as the basis of hypothesis about the independence of a mathematical model (for instance, Newton's gravitation law). The hypotheses about independence arise by observation, by measurements and by measurements processing. However, there exists one more criterion, which influences the forming of hypothesis about independence and, consequently, the forming of corresponding mathematical model.This criterion is the beauty of conceptions, which are the results of modeling. From experience is known, that out of two hypotheses the hypothesis which possesses 'internal beauty', turns out to be more correct then the second one which seems to be more corresponding to the existing measurements.

This criterion is the beauty of conceptions, which are the results of modeling. From experience is known, that out of two hypotheses the hypothesis which possesses 'internal beauty', turns out to be more correct then the second one which seems to be more corresponding to the existing measurements.

The stages of simulation technology:

1. composition of mathematical models;
2. testing mathematical model's closure; elaboration, calculation and processing (usually for computation) of the values of endogenous (inner) characteristics under condition that the values of exogenous characteristics are known;
3. identification of models, i.e. measurement (calculation, certain ways of definition) of the values of the exogenous (outer) characteristics of models;
4. verification of models, i.e. clearing up conditions ensuring correctness of model's prediction;
5. exploitation of the model, i.e. extraction of consequences from model's equations, in particular, realization of calculation of the values of endogenous (inner) characteristics.

The term 'simulation' had been introduced several tens years earlier to designate the method of calculating the average values of characteristics of stochastic phenomena (processes, systems). But the term 'simulation' is used now in the broader sense. The models, which are called sometimes 'simulation model' possess certain qualities from the following set of qualities:

1. complexity of models structure;
2. presence of stochastic exogenous characteristics in model's equations;
3. a great number of endogenous and exogenous characteristics;
4. presence of controls i.e. presence of exogenous characteristics which are chosen by somebody in such way that the properties of phenomena (process, systems) acquire 'desired';
5. impossibility to obtain certain results without computer;
6. the possibility of the model to create 'illusion of reality'

As a rule simulation experiments are carried out within the interactive system containing together with the program for calculating values of endogenous characteristics means for data processing in desirable form, data visualization and manipulation of information in various manner. Such interactive system is called 'practically oriented (problem-oriented) simulation system'.

Mathematical modeling serves as instrument to predict development phenomena (processes, systems). Exploitation of instruments in any field leads to arranging them into structures. Besides infrastructure arise in order to support the original structures. Mathematical modeling is not exception to the rule. In particular, instrumental simulation system arises in order to support elaboration of practically oriented simulation system. Instrumental simulation systems are built over the programming systems and present one of final elements of structure of programming means, ensuring and supporting mathematical modeling.

Investigation in the field of development of technology, which is unity of humanitarian and mathematical methods of analysis and prognosis real phenomena, processes, systems had been initiated by academician N.N. Moiseev. It is described below the concept of relationship between humanitarian and mathematical methods, which are developed in the department now and which are the result of joint work with experts when concrete model had been developed. Some investigations, which were carried out with the use of the technology, which is unity of humanitarian and mathematical methods, are briefly characterized further.

It is evident that there are limits of mathematical models complexity: if the prognosis obtained by mathematical model exceeds these limits there is no pragmatic profit in it. However, sometimes prognosis of development of phenomena (processes, systems) which is too complicate for technologies of mathematical modeling can be obtained by other methods. These 'other' methods of prognosis will be called there 'humanities methods'. So, the methods of prognosis are divided into mathematical and humanities ones. In accordance with this division real phenomena (processes, systems) are divided into 'simple' and 'complex'. (Possibly introduced terminology is not entirely successful. Alternative terminology - mathematical methods of analysis and prognosis are treated as 'rough', humanitarian one - as 'smooth'.) This division is not full: there exist phenomena (processes, systems) for which the development of prognosis cannot be obtained nowdays either by mathematical model or by humanities method. There are phenomena development prognosis of which can be received only using mathematical model. There are phenomena (processes, systems) the prognosis of which can be obtained at present only by means of humanities methods.

The frontier between mathematical and humanities methods of prognosis is not fixed and not too accurate. Development of mathematical modeling technologies leads to invasion into not yet explored fields and there occurs interaction between mathematical and humanities methods.

But division of phenomena (processes, systems) into 'simple' and 'complex' is simplification and is in some sense 'model' of real interaction between mathematical and humanities methods of prognosis. There are two main aspects of this interaction. From the position of the first aspect composing mathematical model start from the humanities analysis of phenomena (processes, systems) under consideration: it is necessary 'to understand' the phenomena, which is subjected to modeling. From the position of the second aspect humanities analysis of results obtained by mathematical modeling have been fulfilled. Also notions (ideas), which arise as a result of this modeling are used in humanities analysis of phenomena (processes, systems) under consideration. It should be added that practically in any phenomena (processes, systems) exist simultaneously 'simple' aspects accessible to mathematical modeling technologies and 'complex' ones which are inaccessible for this technologies. Thus the frontier between mathematical and humanitarian methods of analysis and prognosis 'is washed out' at that in 'both side'. This washing out is process of forming technology, which unify the mathematical and humanitarian methods analysis and prognosis (M-H-technology). It is necessary to note that by terms 'simulation' or 'simulation experiment' often designates the act of exploitation of mathematical model, which is situated on the mobile frontier between mathematical and humanities methods of prognosis of real phenomena (processes, systems). Forming of M-H technology is slow process. Its characteristic duration is comparable with duration of generation life. Therefore the relationship between mathematical and humanitarian methods of analysis and prognosis are often not realized by investigators.

The theme of relationsip between humanitarian and mathematical methods of analysis and prognosis real phenomena, processes, systems are discussed in the publications:

Pavlovsky Yu. N. Simulation models and system. Moscow. Phasis. 2000.131p.(in Russian)

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