In the domain of maritime surveillance, the continuous tracking and monitoring of vessels are imperative for the early detection of potential threats. The Automatic Identification System (AIS) database, which collects vessel movement data over time, including timestamps and other motion details, plays a crucial role in real-time maritime monitoring. However, it frequently exhibits irregular intervals of data collection and intricate, intersecting trajectories, underscoring the importance of analyzing long-term temporal patterns for effective vessel tracking. While Kalman Filters and other physics-based models have been employed to tackle these issues, their effectiveness is limited by their inability to capture long-term dependence and non-linearity in the historical data. This paper introduces a novel approach that leverages Long Short-Term Memory (LSTM), a type of recurrent neural network, renowned for its proficiency in recognizing patterns over extended periods. Recognizing the strengths and limitations of the LSTM model, we propose a hybrid machine-learning algorithm that integrates LSTM with a physics-based model. This combination harnesses the physical laws governing vessel movements alongside data driven pattern mining, thereby enhancing the predictive accuracy of vessel locations. To assess the performance of standalone and hybrid models, various scenarios with different levels of complexity are generated. Furthermore, to simulate real-world data loss conditions often encountered in maritime tracking, temporal data gaps are randomly introduced into the scenarios. The competing approaches are then evaluated using both with time gap and without time gap conditions. Our results show that, although the LSTM model performs better than the physics-based model, the hybrid model consistently outperforms both standalone models across all scenarios. Furthermore, while data gaps negatively impact the accuracy of all models, the performance reduction is minimal for the physics-infused model. In summary, this study not only demonstrates the potential of combining data-driven and physics-based approaches but also sets a new benchmark for maritime vessel tracking.