# Enhanced Location Prediction for Wargaming with Graph Neural Networks and Transformers
## 1 Introduction  
Wargaming, also known as a wargame, is a strategic simulation environment designed for human-machine confrontation, enabling realistic military training and informed decision making [1, 2]. As a typical incomplete information game, it often involves uncertainties, such as unknown enemy force deployments and sizes. With recent advances in data science and artificial intelligence (AI) [3, 4, 5, 6], computerized wargaming has become a challenging platform for studying military intelligence decision making [7, 8, 9]. Through wargaming, complex battlefield situations and emergencies can be simulated, creating a virtual training environment that closely approximates real combat scenarios [10, 11, 12]. These simulations serve as a valuable tool for participants to assess the impact of their decisions, predict strategic outcomes, and test innovative concepts. Moreover, they provide military personnel with the opportunity to analyze potential results and conduct effective training, without the risks and costs of real-world exercises [13, 14]. In tactical wargames, factors such as terrain variation, landforms, buildings, and distance contribute to an inherently incomplete view of the opponent's state. This uncertainty poses significant challenges, requiring agents to make strategic decisions based onlimited or ambiguous data. For intelligent agents aiming to perform at a human-like level, accurately predicting the opponent status or locations under these conditions is crucial for improving the chance of success. By mastering this predictive capability, agents can anticipate opponent moves, formulate effective strategies, and enhance overall performance in complex, adversarial environments. Traditional methods, such as those based on convolutional neural networks (CNNs) [15], have been widely used for location prediction tasks. For example, [PERSON] et al. [16] introduced a method using convolutional encoder-decoders to predict the potential counts and locations of opponent units hidden by the \"fog-of-war\" in StarCraft [5; 6], enabling agents to better estimate enemy positions. To address the challenge of long-term dependencies in such predictions, [PERSON] et al. [17] integrated CNNs with recurrent neural networks (RNNs) [18]. Their experiments demonstrated significant improvements in future state prediction within real-time strategy games. However, the previously mentioned models output potential counts and locations of opponent units as fixed values rather than probability distributions, which can lead to significant deviations under uncertain or incomplete information. To overcome this limitation, [PERSON] et al. [19] developed a framework that was specifically designed to predict the possible location distribution of opponents on the map. Their model incorporates a multi-head input and output structure, along with CNN and gated recurrent unit (GRU) [20] layers, enabling it to handle the complexities of multi-agent interactions and the long-term memory problem. While all previous methods relied on CNN layers to extract spatial features in wargaming, recent advances in graph neural networks (GNNs) [21; 22; 23] have demonstrated superior capabilities in representation learning [24]. GNNs effectively integrate neighboring node information to produce richer, more informative node representations. In the context of wargaming, agents or units can be modeled as nodes within a combat network, where the relationships between them can be learned through a graph structure learning layer [23]. This approach facilitates the application of GNNs to capture complex, multi-agent interactions, thereby enhancing feature representation in wargame environments. Additionally, in wargames, retaining information on the previous status of units is crucial for informed decision making, as well as for making memory networks and attention mechanisms effective tools.