The construction of a mathematical model of a complicated system is often associated with the evaluation of inputs’ (arguments, factors) influence on the output (response), the identification of important relationships between the variables used, and reduction of the model by decreasing the number of its inputs. These tasks are related to the problems of Sensitivity Analysis of mathematical models. The author proposes an alternative approach based on applying Analysis of Finite Fluctuations that uses the Lagrange mean value theorem to estimate the contribution of changes to the variables of a function to the output change. The article investigates the presented approach on an example of a class of fully connected neural network models. As a result of Sensitivity Analysis, a set of sensitivity measures for each input is obtained. For their averaging, it is proposed to use a point-and-interval estimation algorithm using Tukey’s weighted average. The comparison of the described method with the computation of Sobol’s indices is given; the consistency of the proposed method is shown. The computational robustness of the procedure for finding sensitivity measures of inputs is investigated. Numerical experiments are carried out on the neuraldat data set of the NeuralNetTools library of the R data processing language and on data of the healthcare services provided in the Lipetsk region.

As an initial stage prior to Mathematical Modeling, the information processing should provide qualitative data preparation for the construction of consistent models of technical, economic, social systems and technological processes. The question, concerning choosing the most significant input factors affecting the function of the system, is a very actual and important. This problem could be solved with the application of methods of Sensitivity Analysis. The presented paper has the purpose to show a possible approach to this problem through the method of the Analysis of Finite Fluctuations, based on Lagrange mean value theorem, to study the sensitivity of the model under consideration. The numerical example of comparing the results obtained by Sobol sensitivity coefficients, Garson algorithm and proposed approach showed the sustainability of the introduced method. There is shown, that the proposed approach is stable in the sense of applying different input datasets. In particular, the proposed approach has been applied to the construction of a neural network model identifying any anomalies present in certain medical insurances, in order to define the most significant input factors in the anomaly's detecting, discard the others and get a slim and efficient model.

The paper proposes the approach for uniform presentation of technical objects and technological processes with a variable structure. This approach is based on the approximation of specific models describing the object or the process by a uniformed remodeling class. The application of this approach is useful while solving optimization and control problems. Neural network models, which proved their high approximating capability, are suggested as a remodelling class. Application of the given approach is considered by the example of inertial torque transformer (ITT) workflow modelling. This process has a cyclical pattern where each phase of the cycle is divided into four segments described by various systems of nonlinear differential equations with the same parameters. Moreover, the solution to the system describing the next segment depends on the solution to the system obtained by the previous segment. It noticeably makes it difficult to determine the optimum ITT parameters as the fit function has the solution to the system of equations describing the last, the fourth segment of the cycle. The neural network model allows simplifying the solution to the given problem for each cycle segment.

The paper is related to the solution of problems of regulated city intersections and assessment of quality of teaching staff activity. The proposed method of solving these problems - the method of Analysis of finite fluctuations - showed good results represented in the examples below.