Математичне моделювання застосування воєнних ігор під час підготовки військових фахівців

Formulation of the problem in general. In the context of large-scale armed aggression by the russian federation against Ukraine, the urgent task is to explore effective methods for preparing military specialists to address contemporary challenges and threats. The article examines the role of war games in the military education system and their impact on the training of military personnel. The study's primary goal is to develop a comprehensive mathematical model that formalises the process of using war games in military training based on an analysis and prediction of behavioural changes in decision-making. Research methods. A comprehensive methodological approach was applied to achieve the set objective, incorporating mathematical modelling and empirical observation. The study employed methods of stochastic games, Markov decision processes, Bayesian updating, and Q-learning, which facilitated an in-depth analysis of the mathematical description of the military training process. Analysis of recent research and publications. The historical development of war games was analysed, leading to their classification into tabletop, computer-based, and hybrid models used at various training levels to ensure interactivity and realism in the educational process. The study examines these models' features, advantages, and limitations and presents a block diagram illustrating a five-stage process for implementing war games in military training. This process covers cognitive, emotional, and behavioural learning levels. Additionally, approaches to modelling combat scenarios were explored, with particular attention given to applying operational research methods to optimise training. The study identifies regulatory directions for military simulations within the NATO-Ukraine partnership framework. Elements of scientific novelty. The scientific novelty lies in the substantiated and described mathematical apparatus for modelling military personnel's perception of educational material through war games. The proposed mathematical model formalises decision-making and behavioural adaptation, integrating cognitive and operational factors to enhance training efficiency. Theoretical and practical significance of the article. The research contributes to the theoretical foundation of military training by providing a structured methodology for implementing war games in professional education. Practically, the findings support the integration of war games as an effective tool for improving strategic decision-making skills among military officers. The proposed approach also emphasises the importance of adapting training methods to modern combat realities and regulatory frameworks. Conclusion and the perspectives of future research. The study concludes that the combination of traditional and modern digital war game methods enhances the effectiveness of military commanders' training and improves strategic decision-making skills. Future research may focus on adapting military simulations to the realities of modern warfare, refining their classification, and improving existing training methodologies, tools, and techniques. The importance of incorporating advanced technologies, such as artificial intelligence, virtual reality, and augmented reality, is substantiated, as these innovations will further develop war game-based training models and enhance the preparation of military specialists.