# A Hybrid Deep Learning-Based Load Forecasting Model for Logical Range
## 1 Introduction  
In recent years, enhancing the capability of test and training operations under integrated land, sea, air, space, and electromagnetic warfare environments has become a focal point in military competition. To support such complex missions, the concept of the Logical Range has emerged. A Logical Range is a mission-oriented, reconfigurable range system that integrates testing, training, and simulation resources through distributed networking and high-performance computing technologies [1, 2]. Unlike traditional test ranges, Logical Ranges can dynamically reorganize functional elements across geographically dispersed platforms to meet the demands of new tasks that a single range cannot fulfill alone. This flexible architecture enables cross-domain resource integration and real-time mission composition, but it also presents new technical challenges. During joint operations, such as cross-regional flight testing or collaborative weapon system evaluation, Logical Range platforms often suffer from uneven workload distribution, high concurrency, and complex system heterogeneity. These factors can cause delays in task scheduling and execution, leading to reduced responsiveness and efficiency. Consequently, accurate load forecasting becomes crucial for optimizing task allocation and maintaining system stability under fluctuating conditions. Although traditional statistical approaches [3, 4, 5, 6] have been applied for time-series load prediction, they typically rely on strict assumptions (e.g., Poisson distribution) and fail to handle the stochastic, nonlinear nature of real-world Logical Range workloads [7]. To overcome these limitations, more adaptable, learning-based forecasting frameworks are needed to support intelligent resource scheduling in such dynamic environments. To capture temporal patterns in such data, autoregressive models and probabilistic statistical approaches [8; 9; 10; 11] have been employed with some success. However, in dynamically evolving Logical Range environments, their predictive performance often deteriorates due to their limited adaptability to abrupt changes and temporal nonstationarity [12]. Recently, deep learning-based prediction models--notably those based on recurrent neural networks (RNNs)--have demonstrated strong capabilities in learning nonlinear temporal dependencies directly from historical data [13; 14; 15; 16; 17; 18]. Nevertheless, many of these approaches fail to account for spatial correlations that may exist across subsystems or geographically distributed nodes. Recent studies have highlighted the importance of jointly modeling both spatial and temporal features, which can significantly improve the accuracy of forecasting in nonstationary and highly volatile load environments [19]. To address the aforementioned challenges, we propose GCSG: a novel hybrid deep learning model that integrates Gramian Angular Field (GAF) encoding, a Convolutional Neural Network with Squeeze and Excitation (CNN-SENet), and a Gated Recurrent Unit (GRU). This model is specifically designed to handle the complexity of load forecasting in Logical Range environments, offering several key innovations:  
First, we employ the GAF approach to transform 1D nonstationary load sequences into 2D images, enabling CNNs to effectively capture spatial correlations. Second, we develop a CNN-SENet module that adaptively recalibrates channel-wise feature responses, enhancing the model's ability to focus on informative features while suppressing noise, which is crucial for robust feature extraction in complex environments. Finally, we introduce an attention-based spatiotemporal fusion mechanism that dynamically combines spatial features (from CNN-SENet) with temporal dependencies (from GRU), significantly improving the prediction accuracy under highly dynamic workloads by capturing both transient patterns and long-term trends in the data. The main contributions of this study are as follows:  
1. We propose a domain-specific hybrid forecasting model tailored to the Logical Range context.