a number of combinations of M by 2. The = M / D ; with Mg being a scale process of training SOM is described, first, g g g with a neighborhood of interaction of kth quotient, D – a value of fractal dimension of a neural processing element with ith training deviations temporal series. The table represents an optimal plan of audits and a value of tax dk i sampling vector hk i = exp(- ), with dk i additional charges (in rubles), obtained as a result of audits (first 12 enterprises are shown being a distance of interaction according to according to the -criterion and 12 ones with Euclidean measure; being a parametric biggest additional charges). As it is seen, variable of Gaussian distribution:

enterprises out of 12 ones that made a flagrant t breach of tax laws occured into the audit plan. (t) = exp(- ), t = 0,1,2,... is an 0 Table. Comparing modelling results with results of field tax audits. initial value of ; 1 is a certain parameter influencing performance. Second, with a Additional speed of weights change during the training of g No. No. charges a training sample described with a (t) 11 0.20276 11 parametric variable exponentially differing 3 0.09776 9 from the repeat run number:

22 0.07272 8 t (t)=0 exp(- ), t = 0,1,2,..., with 9 0.06346 24 14 0.04393 21 being one more parametric variable 21 0.02258 22 8 0.02081 16 influincing the effectiveness of SOM 24 0.01875 10 algorithm work.

2 0.01612 13 1371761 When forming a Bayesian set of 12 0.01565 3 hypotheses {hq} training parameters varied 30 0.01513 14 discontinuously on three levels:

Материалы XVI Международной конференции по нейрокибернетике Conference “Neuroinformatics-2002”. Lectures on Thus a set of 9 NN was grouped. 3 backup neuroinformatics. Part 2. Moscow. Moscow Engineering trainings were carried out for each qth network.

and Physics Institute, 2002. – pp.30-93.

All comparable hypotheses (NN) {h } passed q 3. Neural network modelling in tasks of ranking and clustering in budget and tax systems of regional and the selection condition by criterion. The q municipal levels (in Russian) / S.A.Gorbatkov, D.V.Polupanov and others. – UFA: Bashkir State averaged value of this criterion equals 0.University Editorial and Publishing Center, 2011. – which tells us about a quite high clustering pp.

quality.

4. S.A.Gorbatkov, I.I.Beloliptsev, S.A.Farkhieva, D.V.Polupanov. An estimation of algorithms of preList of references regulation and Bayesian regularizing neural networks for an office tax audit (in Russian). // XIV All-Russian Scientific and Technical Conference “Neuroinformatics1. S.A.Gorbatkov, D.V.Polupanov. The regularization 2012”: Collected articles. Part. No.. – Moscow: National of neural network models for economic objects with a Research Nuclear University of Moscow Engineering and strong data distortion (in Russian) // Proceedings of XV Physics Institute, 2012. – pp. 38-48.

International Cybernetics Conference. Vol. 2. "Brain5. I.V.Shevchenko, A.A.Khalafyan, E.U.Vasilyeva.

Computer Interface” Symposium, 3rd Symposium for Creating a virtual client base for analysing solvency of Neuroinformatics and Neurocomputers. Rostov-on-Don.

Russian enterprises (in Russian) // Finance and Credit, Southern Federal University publishing house. 2009. – 2010, No.1 (385). – pp. 13-18.

pp. 263- 2. S.A.Shumsky. Bayesian regularization of training (in Russian) // IV All-Russian Scientific and Technical 4-Й МЕЖДУНАРОДНЫЙ СИМПОЗИУМ «НЕЙРОИНФОРМАТИКА И НЕЙРОКОМПЬЮТЕРЫ» NEURO-NET FORECASTING AS EVOLUTIONARY INTELLECTUAL PROCESS O.M. Maximova Institution of Civil Engineering, Siberian Federal University, Krasnoyarsk maximom_7@mail.ru The evolutionary model of neuro-net forecasting However well-known conventional corresponding to the dialectics of knowledge and ideas forecasting methods represent single of evolutionary cybernetics is suggested. In contrast to extrapolation of some functions, constructed the traditional approach it permits to achieve a on approximation of known information in considerable depth of forecasting. This evolutionary model of forecasting is realized on the base of neuro-net given region (e.g., in virtue of Lagrange technology as the step process with teaching. Its interpolation polynomials, etc.).

effectiveness is illustrated by examples of mathematical, It is established in the context of nonlinear mechanical and structural problems.

dynamics development [2], that “fundamental Introduction constraints are determined for predictability of the complex systems”, “their behavior can be It has been known [1] that traditional forecasted only for short time interval” and technique for the complex objects theoretical “for every system there is its own forecast model creation consists in adequate model horizon”.

construction at once for set level complexity.

To validate results in any dynamic system, An alternative modern technique consists in for any modelled entity, the general acceptance of various quite simple models as a mathematical model approach is used in base and supplement to them of the derivative nonlinear dynamics: the motion of particle in laws, borrowed from the nature or engineering.

phase space, the dimension of which is defined In this case the problem of the complex system by number of variables that determine the model construction reduces to “raising” of the system state. The quality of the model being model from easier system by evolutional used is neither analyzed nor discussed.

method [1].

Such approach to forecasting model is in a The use of neuro-net, trained on the basis of certain sense traditional and is quite popular.

input information with subsequent teaching in The model neither changes in the course of accordance with obtained while in operation forecasting, nor progresses. So in the paper [3] additional data, in terms of process simulation valuable information is contained about is a dialectical process of evolutive simulation, information gaining in short adjacent zone and corresponding to evolutionary cybernetics model teaching with regard to fresh concepts, system approach, and fully accords information, but forecast process itself is to the dialectical-materialist theory of realized during one step.

knowledge.

In other words, the critical weakness of Traditional approach to the forecasting traditional methods is the fact that for model information gaining (i.e. forecasting) an outForecasting is the most important dated system (model and synaptic junctions) is component of theory of knowledge. Planning used, which ignores process innovation. Thus, and projecting of system’s development dialectical relationship between information occurring processes is impossible without it.

(as material element) and a system, its An importance and significance of forecasting structure, is violated, and the point is that its for modern stage are incontestable.

evolution is not provided.

Forecasting went from the domain of science System approach to the forecasting model to the stage of technology and future Forecasting model in terms of the projecting in the various realms of science, materialist dialectic of knowledge. System engineering, native and social processes. At approach with regard to the laws of systems present jump in forecasting is observed.

development application [4] to understanding of all above-mentioned makes it possible to Материалы XVI Международной конференции по нейрокибернетике distinguish the following characteristics of the intellectual evolutionary process of cognition evolutionary cognition process, being used in and is convenient for this purposes.

forecasting: Indeed, the use of this neuro-net forecasting model allows efficiently realize:

• gradual accumulation of input information, and its processing to user-friendly • approximation of experimental format; and other discrete data of initial information - neuron network teaching;

• appropriate modernization (improvement) of cognition model • additional data generation in a (forecasting instrument); given region, including in the neighborhood of borders by interpolation of given taught • consequent (step-by-step) neuron network - neuron network spiral-shaped decision making and decision functioning;

correcting process with regard to system’s laws of development. • information gaining out of the Thus, in principle forecasting represents region borders (to short distance) some informational process, during which extrapolation;

accumulation of information and altering takes • neuron network correction place. But in [2], for example, initial (teaching) with regard to interpolation and mathematical model is not corrected in the extrapolation data with effective use of the process of this information accumulation and preceding synaptic junction chart (in addition depends only on initial information data. This the known far check points can be taken into serious dialectic contradiction of cognitive account);

process is similar to the state of statuesque • further transition to the next moving process stationary observer; it process step, which repeats above mentioned naturally leads to some limitary observation procedures.

horizon.

Thus, spiral-shaped step-by-step process, It’s possible to express such treatment of including gradual information addition and forecasting by conditional formula (1) in cognitive model updating (teaching) on its contrast to the formula (2), wherein model base, is realized. In case of stepwise behavior depends on altering in the process of forecasting “onlooker” is (intellectual forecasting researcher) as if moving step-by-step along F(M(x), I); (1) with process (it does not stand on one place), F(M(x,I), I), (2) i.e. forecasting is realized dynamically.

where x – parametric variables of the phase Therefore the effect (it is the author's space, M – model, I – information, F – opinion that it is false), on which it is pointed forecasting.

out in the Ref. [2], about presence of barrier The model ability to be taught in the (horizon), beyond which forecasting is process expresses one of the most important impossible, does not arise.

properties of intelligent system (2) in contrast Note, that if special data refinement on the to (1), devoid of these properties. Thus the basis of experiment will be included in the approach (1) ignores the past of the system, stepwise prediction process (or on the basis of which can be used for the test check.

some other objective data), then accumulation of errors will not take place and the stepwise Step-by-step model of neuro-net prediction will successfully proceed.

forecasting in exemplification of evolutional Thus, fundamental nature of suggested cybernetics. Neuro-informatics and its problem consists in formation of process close methods, due to possibility to be taught, are an to the intellectual process, improving in intelligent system type and represent a accordance with the concepts of evolutional convenient universal instrument for cybernetics. A forecasting model must include approximation, which takes into account main features of the dialectical-materialist various process regularities (although intellectual cognition process.

implicitly). Therefore we can insist that elaborated step-by-step model of neuro-net forecasting [4-8] corresponds to the 4-Й МЕЖДУНАРОДНЫЙ СИМПОЗИУМ «НЕЙРОИНФОРМАТИКА И НЕЙРОКОМПЬЮТЕРЫ» Step-by-step neuro-net forecasting forecasting process is led to the execution of method description operations, described in steps 1, 2, and so on.

Such step-by-step neuro-net forecasting is Neuro-network methodology permits to well adapted to continuous, quite smooth solve not only interpolation problems, but processes, elaborated by multidimensionality extrapolation ones as well. If a neuro-net and multiparameter properties. Targeted to interpolation guarantees a good accuracy of desired far orientation points neuro-net solutions, then a traditional neuro-net forecasting is possible, as well as the choice of extrapolation doesn’t do it and permits an optimal forecasting trajectory, satisfying to forecasting only in the nearest border zone.

specified criterion extremum. Another Therefore the practical neuro-net forecasting information tasks which are characterized by method (Fig. 1), having considerably greater bifurcations, jumps, discontinuity have not possibilities and advantages, is suggested. It is been investigated yet, but the suggested achieved by means of the above mentioned approach allows detect process tendency to neuro-net technology properties use: (see sec.

formation of such specialities.

2). Besides, the whole process is realized Stepwise process of neuro-net forecasting at uniformly with taking different restrictions this stage is human-aided. In future it is contained in the teaching pattern into account.

possible to substitute dialog mode by 1 2 generatio neuron network automatic one, wherein human quantum is n of initial network functioning near pattern teaching border zone reduced to necessary minimum of control.

Adding an obtained Application example of step-by-step 6 current teaching forecast to human information the forecasting for engineering structures being addition teaching pattern pattern Step-by-step method of neuro-net forecasting has been tested and used to additional neuron tridimensional engineering structures, namely network control of to forecasting its stress and strain state (SSS) accuracy 7 obtaining for long- and short-term static load.

It is possible to associate engineering exit structures with so-called complex systems.

Structural complexity, complexity of Fig.1. Step-by-step neuro-net forecasting scheme in a dialog mode functioning, development etc. are included into the concept of complexity. It is necessary The step-by-step method of neuro-net to estimate and forecast their factual technical forecasting consists of the following steps.

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