Yuri G. Rykov

Keldysh Institute of Applied Mathematics RAS

Currently, the methodology of artificial intelligence is gaining more and more applications. Neural networks (NN) attract a lot of attention. One of the main reasons for this is that the NN technology is, in a sense, universal. On the other hand, some other computer technologies, having the nature of artificial intelligence or others, also have the properties of universality. In the context of this article, these are technologies of fuzzy cognitive maps (FCM) and special systems of partial differential equations, so called “systems of conservation laws” (CL). All the approaches just mentioned are used to develop models of complex systems (CS), i.e. aggregates of a large number of elements with connections between them of various types. The specificity of the CL theory, which is able to model joint balances of various quantities on the level of physical processes, lies in the presence of nonlinear effects, such as the formation of singularities in solutions. The FCM technology allows for an extension of the original concept by B. Kosko with a wider range of interpretation. The article provides an illustration of how these technologies can be combined into a single methodology for creating a modeling medium for the CS based on the NN approach.

complex systems, computer science, modeling media, fuzzy cognitive maps, weighted digraph, graph partitioning by cycles, conservation laws, variational representation, neural networks for conservation laws