Distributed computing platforms provide a robust mechanism to perform large-scale computations by splitting the task and data among multiple locations, possibly located thousands of miles apart geographically. Although such distribution of resources can lead to benefits, it also comes with its associated problems such as rampant duplication of file transfers increasing congestion, long job completion times, unexpected site crashing, suboptimal data transfer rates, unpredictable reliability in a time range, and suboptimal usage of storage elements. In addition, each sub-system becomes a potential failure node that can trigger system wide disruptions. In this vision paper, we outline our approach to leveraging Deep Learning algorithms to discover solutions to unique problems that arise in a system with computational infrastructure that is spread over a wide area. The presented vision, motivated by a real scientific use case from Belle II experiments, is to develop multilayer neural networks to tackle forecasting, anomaly detection and optimization challenges in a complex and distributed data movement environment. Through this vision based on Deep Learning principles, we aim to achieve reduced congestion events, faster file transfer rates, and enhanced site reliability.