# Enhanced Location Prediction for Wargaming with Graph Neural Networks and Transformers
## 1 Introduction
Transformers [25] have since proven highly effective in multi-agent environments, such as in real-time strategy games [6], multi-agent motion prediction [26; 27], and trajectory prediction [28; 29; 30]. Specifically, [PERSON] et al. [31] proposed the multi-agent transformer (MAT) model based on the transformer architecture to model interactions between agents. HiVT [27] focuses on learning complex patterns in multi-agent systems through using a hierarchical structure in the transformer model to process motion trajectories over time. MART [30] employs deep learning models to predict the spatial trajectory of an agent by leveraging historical movement data, and this is achieved using RNNs or transformers. These models, particularly through attention mechanisms, excel at modeling long-range dependencies and temporal dynamics, making them highly suitable for tasks like location prediction in wargaming scenarios. As a core component of transformer architectures, the multi-head self-attention (MSA) mechanism enables the model to extract diverse characteristics of input data from multiple perspectives simultaneously [32]. Each attention head learns distinct aspects of the sequence, offering a comprehensive understanding of the data. Compared to traditional RNNs, MSA processes all of the sequence elements in parallel, significantly improving the computational efficiency and scalability. While motion and trajectory prediction are more focused on the continuous and spatial aspects of agent movement in a given environment, often with predictable or known dynamics, location prediction [19; 33; 34] (our focus) in wargames extends beyond simple motion forecasting to consider strategic decision making. In wargames, agents must predict enemy locations while accounting for uncertainty and adversarial behaviors. Predicting the locations of opponent units is a critical yet challenging task, especially when relying on situational data provided by tactical wargame systems. One challenge arises from the high redundancy of data in consecutive frames, where the positions of units may remain unchanged or show minimal variation over time, resulting in substantial repetitions. In addition, opponent units occupy a small proportion of the overall map data and are distributed sparsely across the map, leading to a highly sparse data structure. To address these issues, we propose an enhanced location prediction model (ELP-Net) that integrates GNNs and transformers. The model is particularly adept at capturing complex inter-node relationships, allowing one to extract valuable information from a redundant and sparse data environment. Our main contributions are as follows. * Temporal sequence modeling with transformers: ELP-Net incorporates a transformer module to handle temporal sequence data, enabling the simultaneous consideration of information from multiple units across different time steps. This results in richer feature extraction by capturing the temporal dynamics within the wargame. * Spatial-temporal GNN-based model: The core advantage lies in the combination of a temporal module with a graph convolution module, incorporating the novel mix-hop attention propagation layers. This design outperforms traditional CNNs in handling sparse data and capturing complex node relationships, providing a more robust solution for location prediction. * End-to-end graph sequence learning framework: The graph structure learning layer, the graph convolution, the temporal convolution modules, and the transformer architecture are integrated and jointly optimized within an end-to-end learning framework. * Enhanced location prediction performance: Numerical experiments have demonstrated that ELP-Net consistently outperforms baseline models, underscoring the effectiveness of its integrated architecture in accurately capturing spatial-temporal dependencies and providing reliable predictions in complex wargaming scenarios. The remainder of this work is organized as follows.