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The paper proposes a new approach to constructing a decentralized hierarchical network of modular type for solving complex problems in the paradigm of training artificial neural networks (ANN) with a teacher. The main idea of the proposed approach to solving the problem is the formation of a system model in the form of a multilevel hierarchical network, consisting of typical autonomous modules built on an ANN of two configurations: а coordinator and a terminal model. The coordinator is a specially designed ANN, which forms, based on the target set of its level, the target set of the next subordinate level of the network hierarchy. The terminal model is a traditional ANN of any architecture and organization of the learning process. The proposed hierarchical structure of the network allows solving a complex initial problem asynchronously in time and in parallel in space, using distributed computing resources and geographically dispersed teams of researchers. The paper provides an example of numerical modeling that demonstrates the proposed approach for the synthesis of a multilevel hierarchical network and confirms all the declared and expected results of its use. [ABSTRACT FROM AUTHOR]