Md Mahbub Alam

Md Mahbub Alam, Amilcar Soares, José F. Rodrigues-Jr et al.

Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints, leading to forecasts that disobey vessel motion dynamics, such as in scenarios with limited or noisy data where sudden course changes or speed variations occur due to external factors. To address this limitation, we propose a Physics-Informed Neural Network (PINN) approach for trajectory prediction that integrates a streamlined kinematic model for vessel motion into the neural network training process via a first- and second-order, finite difference physics-based loss function. This loss function, discretized using the first-order forward Euler method, Heun's second-order approximation, and refined with a midpoint approximation based on Taylor series expansion, enforces fidelity to fundamental physical principles by penalizing deviations from expected kinematic behavior. We evaluated PINN using real-world AIS datasets that cover diverse maritime conditions and compared it with state-of-the-art models. Our results demonstrate that the proposed method reduces average displacement errors by up to 32% across models and datasets while maintaining physical consistency. These results enhance model reliability and adherence to mission-critical maritime activities, where precision translates into better situational awareness in the oceans.

Md Mahbub Alam, Jose F. Rodrigues-Jr, Gabriel Spadon

Accurate vessel trajectory prediction is essential for enhancing situational awareness and preventing collisions. Still, existing data-driven models are constrained mainly to single-vessel forecasting, overlooking vessel interactions, navigation rules, and explicit collision risk assessment. We present a transformer-based framework for multi-vessel trajectory prediction with integrated collision risk analysis. For a given target vessel, the framework identifies nearby vessels. It jointly predicts their future trajectories through parallel streams encoding kinematic and derived physical features, causal convolutions for temporal locality, spatial transformations for positional encoding, and hybrid positional embeddings that capture both local motion patterns and long-range dependencies. Evaluated on large-scale real-world AIS data using joint multi-vessel metrics, the model demonstrates superior forecasting capabilities beyond traditional single-vessel displacement errors. By simulating interactions among predicted trajectories, the framework further quantifies potential collision risks, offering actionable insights to strengthen maritime safety and decision support.

Md Mahbub Alam, Luis Torgo, Albert Bifet

Due to the surge of spatio-temporal data volume, the popularity of location-based services and applications, and the importance of extracted knowledge from spatio-temporal data to solve a wide range of real-world problems, a plethora of research and development work has been done in the area of spatial and spatio-temporal data analytics in the past decade. The main goal of existing works was to develop algorithms and technologies to capture, store, manage, analyze, and visualize spatial or spatio-temporal data. The researchers have contributed either by adding spatio-temporal support with existing systems, by developing a new system from scratch for processing spatio-temporal data, or by implementing algorithms for mining spatio-temporal data. The existing ecosystem of spatial and spatio-temporal data analytics can be categorized into three groups, (1) spatial databases (SQL and NoSQL), (2) big spatio-temporal data processing infrastructures, and (3) programming languages and software tools for processing spatio-temporal data. Since existing surveys mostly investigated big data infrastructures for processing spatial data, this survey has explored the whole ecosystem of spatial and spatio-temporal analytics along with an up-to-date review of big spatial data processing systems. This survey also portrays the importance and future of spatial and spatio-temporal data analytics.