Reduction of hierarchical models: researching sensitivity by factors using analysis of finite fluctuations
- Authors: Sysoev A.S.1, Pogodaev A.K.1, Saraev P.V.1
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Affiliations:
- Lipetsk State Technical University
- Issue: No 113 (2025)
- Pages: 21-36
- Section: Systems analysis
- URL: https://journal-vniispk.ru/1819-2440/article/view/289705
- ID: 289705
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Abstract
The selected class of mathematical models determines the methods used in the study of a system or process and approaches to their control. One of the directions of model structure control is its reduction, understood as a reduction in the number of factors in order to build a less computationally expensive model. This problem can be referred to the concept of mathematical remodeling --- building a new model on the basis of a known one. Among the ways of solving such a problem is the Sensitivity Analysis of the model by factors, which can be carried out in various ways. One of these ways is based on applying the method of Analysis of Finite Fluctuations to estimate sensitivity measures. This method is based on the use of Lagrange mean value theorem. The mentioned theorem delivers an exact decomposition of the finite increment of a model's response as a weighted sum of the finite increments of its factors. The paper describes an approach that allows performing Sensitivity Analysis of this type at each of the levels of a hierarchical system, as well as an end-to-end analysis that involves finding estimates of the influence measures of the model outputs of the preceding levels on the output of the model of the upper level. Numerical examples demonstrating the applicability of the method are presented. Classical full-connected neural networks are used as a class of models describing the hierarchical levels of the system.
About the authors
Anton Sergeevich Sysoev
Lipetsk State Technical University
Email: sysoev_as@stu.lipetsk.ru
Lipetsk
Anatoly Kir'yanovich Pogodaev
Lipetsk State Technical University
Email: pak@stu.lipetsk.ru
Lipetsk
Pavel Viktorovich Saraev
Lipetsk State Technical University
Email: psaraev@yandex.ru
Lipetsk
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