A Retrieval-Enhanced Transformer for Multi-Step Port-of-Call Sequence Prediction in Global Liner Shipping

Accurate long-term trajectory prediction for maritime vessels is essential for safety and logistical efficiency. While deep learning models, particularly Transformers, have shown promise in processing Automatic Identification System (AIS) data, they often struggle with the quadratic computational complexity of self-attention and the loss of accuracy over extended forecasting horizons. This study proposes TempTPI, a novel prediction framework that integrates an Informer-based encoder with a multi-channel temporal encoding mechanism. The Informer architecture leverages a ProbSparse self-attention mechanism to reduce computational overhead and focus on the most significant dependencies, while the temporal encoder utilizes Fourier-like frequency expansions to capture cyclic patterns (hourly, daily, and seasonal) in vessel behavior. We evaluate our model against the state-of-the-art TPTrans architecture using AIS data from Danish waters. Experimental results demonstrate that TempTPI consistently outperforms existing methods across prediction windows of 1 to 5 hours. Notably, at a 5-hour horizon, the proposed model achieves a 55% improvement in Mean Squared Error (MSE), offering a robust solution for long-range maritime situational awareness.

To address the challenges of behavioral multimodality, limited semantic utilization, and long-term error accumulation in vessel trajectory prediction, this paper proposes M3-Former, a multimodal trajectory prediction framework enhanced by large language models (LLMs). The proposed framework incorporates vessel static attributes and navigational intent as semantic priors for long-term trajectory modeling. Specifically, a unified multimodal representation space is constructed, in which static semantic information is encoded by a pre-trained LLM and aligned with dynamic trajectory features through self-attention. To jointly capture global route planning and local motion variations, a dual-granularity Mixture-of-Experts (MoE) architecture is introduced, where sequence-level experts model global navigation trends and token-level experts refine fine-grained maneuvering behaviors. In addition, a Steering-Weighted Cross-Entropy loss is designed to alleviate the long-tail distribution of sparse turning samples and improve prediction accuracy in critical maneuvering scenarios. Experiments on a real-world Danish AIS dataset demonstrate that M\textsuperscript{3}-Former consistently outperforms state-of-the-art baselines across prediction horizons from 1 to 4 hours. In the 4-hour prediction task, the proposed method reduces Average Displacement Error (ADE) and Final Displacement Error (FDE) by 4.4% and 5.1%, respectively, compared with the strongest baseline. Qualitative and ablation analyses further verify that semantic fusion effectively reduces long-term trajectory drift, while the dual-granularity MoE improves robustness in complex waterways and route-branching scenarios. The proposed framework establishes a semantic-guided hierarchical prediction paradigm, in which high-level navigational intent and local motion dynamics are jointly modeled for robust long-term vessel trajectory forecasting.

Long-horizon maritime trajectory prediction is important for shipping management, logistics planning, and maritime risk analysis, yet month-level forecasting remains insufficiently studied. Existing deep learning methods mainly focus on short- and mid-term coordinate extrapolation and often struggle to preserve route feasibility and destination correctness over extended horizons. This paper investigates joint long-horizon vessel trajectory and destination forecasting with reasoning-capable large language models, and develops a Maritime LLM post-training framework based on Reinforcement Learning with Verifiable Reward (RLVR). An AIS-based benchmark is constructed with 60-day historical trajectories and 30-day forecasting horizons, where trajectories are converted into semantic textual representations for RL prompt construction. RLVR aligns LLMs with maritime forecasting objectives by enforcing physical validity, providing early-weighted trajectory supervision, and evaluating destination correctness through hierarchical matching and curriculum learning. Experimental results show that RLVR-trained LLMs substantially improve over zero-shot LLMs and representative deep learning baselines, especially on destination-related metrics. Among the evaluated RLVR-trained variants, 4B LLMs achieve the best overall performance, suggesting that reward-compatible optimization and task-specific capacity matching are more important than simply using larger 8B or 14B LLMs. The results also show that LSTM remains a strong deep learning baseline under limited fine-tuning data, while Transformer-style spatio-temporal models typically require larger datasets and richer structured inputs. Overall, this work advances semantic, verifier-aligned maritime forecasting for operational decision support.