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Ranking vertices of multidimensional networks is crucial in many areas of research, including selecting and determining the importance of decisions. Some decisions are significantly more important than others, and their weight categorization is also imortant. This paper defines a completely new method for determining the weight decisions using artificial intelligence for importance ranking of three-dimensional network vertices, improving the existing Ordered Statistics Vertex Extraction and Tracking Algorithm (OSVETA) based on modulation of quantized indices (QIM) and error correction codes. The technique we propose in this paper offers significant improvements the efficiency of determination the importance of network vertices in relation to statistical OSVETA criteria, replacing heuristic methods with methods of precise prediction of modern neural networks. The new artificial intelligence technique enables a significantly better definition of the 3D meshes and a better assessment of their topological features. The new method contributions result in a greater precision in defining stable vertices, significantly reducing the probability of deleting mesh vertices., Comment: 8 pages, 4 figures