In this research study, we investigate the ability of deep learning neural networks to provide a mapping between features of a parallel distributed discrete-event simulation (PDDES) system (software and hardware) to a time synchronization scheme to optimize speedup performance. We use deep belief networks (DBNs). DBNs, which due to their multiple layers with feature detectors at the lower layers and a supervised scheme at the higher layers, can provide nonlinear mappings. The mapping mechanism works by considering simulation constructs, hardware, and software intricacies such as simulation objects, concurrency, iterations, routines, and messaging rates with a particular importance level based on a cognitive approach. The result of the mapping is a synchronization scheme such as breathing time buckets, breathing time warp, and time warp to optimize speedup. The simulation-optimization technique outlined in this research study is unique. This new methodology could be realized within the current parallel and distributed simulation modeling systems to enhance performance.