Earthquake early warning systems play crucial roles in reducing the risk of seismic disasters. Previously, the dominant modeling system was the single-station models. Such models digest signal data received at a given station and predict earth-quake parameters, such as the p-phase arrival time, intensity, and magnitude at that location. Various methods have demonstrated adequate performance. However, most of these methods present the challenges of the difficulty of speeding up the alarm time, providing early warning for distant areas, and considering global information to enhance performance. Recently, deep learning has significantly impacted many fields, including seismology. Thus, this paper proposes a deep learning-based framework, called SENSE, for the intensity prediction task of earthquake early warning systems. To explicitly consider global information from a regional or national perspective, the input to SENSE comprises statistics from a set of stations in a given region or country. The SENSE model is designed to learn the relationships among the set of input stations and the locality-specific characteristics of each station. Thus, SENSE is not only expected to provide more reliable forecasts by considering multistation data but also has the ability to provide early warnings to distant areas that have not yet received signals. This study conducted extensive experiments on datasets from Taiwan and Japan. The results revealed that SENSE can deliver competitive or even better performances compared with other state-of-the-art methods.