Analysis of Complex Poorly Formalized Natural Engineering Systems Using Cognitive Modeling Technology

• Published in: Mathematical models and computer simulations Vol. 17; no. 4; pp. 449 - 459
• Main Authors: Baluta, V. I., Varykhanov, S. S., Osipov, V. P., Rykov, Yu. G., Chetverushkin, B. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.08.2025; Springer Nature B.V
• Subjects: Apexes; Complex systems; Graph theory; Graphical representations; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Neural networks; Permafrost; Simulation and Modeling; a complex weakly formalized system; graph partitioning into cycles; weighted digraph; activation function; natural-technical system; degree of influence; cognitive factor modeling; weakly structured situation
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S207004822570019X

At the mathematical level of rigor, the structure of the cognitive factor model of a complex weakly formalized system (CWFS) is described in the case of using the nonlinear activation function ReLU. The methodology of constructing this model is a generalization of the previously developed approach of the authors, which allows strict estimates using a nonlinear activation function, which is often used in the construction of neural networks. A complex system is represented as a directed graph, the vertices and edges of which are assigned certain values. The article defines a nonlinear procedure for calculating the values of the system’s elements (internal vertices) on a graph depending on external factors (input vertices) and, accordingly, calculating the coefficients of the degree of influence introduced by the authors earlier. In contrast to the linear case, in the nonlinear case, the coefficients of the degree of influence significantly depend on the values of the vertices—elements of the system. As an example, a model natural-technical system related to the determination of the stability of infrastructure facilities built on permafrost soils is studied.