Abstract: The object of the study is mathematical modeling methods. The subject of the study is the application of mathematical methods in modeling digital twins of a social group. The aim of the work is to model the digital counterparts of a social group. A digital double is a digital copy of a physical object or process, with the right approach, it helps to improve the main and auxiliary business processes. This concept is part of the fourth industrial revolution and is designed to help detect problems faster, find out what will happen to the original in different conditions and, as a result, produce better products. In this article, some applied aspects are considered, the main provisions of the mathematical theory of digital twins of social groups are presented. To solve the problem of creating a digital double of a social group (students) as one of the tools, the authors proposed to use the technologies of population algorithms. The novelty of the research consists in the application of the swarm part algorithm for modeling digital twins of a social group. The particle swarm method was chosen as a research tool. As the social group under study finds the optimal position in space, so the element of the digital twin of the particle swarm model based on them can search in space, in particular, the extremes of functions. Which, for example, is applicable to finding the minimum of the loss function in machine learning. A graphical simulation in the Java Script language was performed using the three library.js. Data processing was performed using the C# Job System, which provides parallelization of computing processes and is integrated into the Entity Component System. A program was implemented that simulates the activity of a student group as one of the constituent elements of a digital twin of a social group. Swarm algorithms are promising in the field of practical application. On their basis, it is possible not only to solve the problems of digital twins, but also to manage groups of robots, robotic systems and complexes.