Enhancing Global Maritime Traffic Network Forecasting with Gravity-Inspired Deep Learning Models

TL;DR

This paper addresses the global risk of non-indigenous species (NIS) spread via ballast water carried by maritime shipping and proposes a physics-informed, gravity-inspired workflow to forecast port-to-port traffic. It introduces Transformer Gravity, a transformer-based extension of gravity models that captures short- and long-term dependencies in vessel flows, and couples a link-prediction step to identify probable origin–destination pairs before applying gravity-based predictions. The model leverages bilateral trade data and graph metrics from the global shipping network, and demonstrates superior predictive performance, achieving a cross-validated CPC of 0.864 for 3- and 5-layer variants, with NRRMSE = 0.080 and Corr = 0.977, and a test CPC of 0.848; it also attains an environmental-distance correlation of $r = 0.889$ with true flows, indicating strong alignment in risk assessment. The work supports more accurate ballast water risk management and policy-making by highlighting high-risk invasion pathways and enabling data-driven monitoring under evolving global trade conditions, while remaining adaptable to additional data sources and contexts. Additionally, the approach yielded 89% binary accuracy for distinguishing existing vs. non-existing trajectories and 84.8% accuracy for predicting vessel counts between key port areas, representing meaningful gains over traditional deep-gravity models.

Abstract

Aquatic non-indigenous species (NIS) pose significant threats to biodiversity, disrupting ecosystems and inflicting substantial economic damages across agriculture, forestry, and fisheries. Due to the fast growth of global trade and transportation networks, NIS has been introduced and spread unintentionally in new environments. This study develops a new physics-informed model to forecast maritime shipping traffic between port regions worldwide. The predicted information provided by these models, in turn, is used as input for risk assessment of NIS spread through transportation networks to evaluate the capability of our solution. Inspired by the gravity model for international trades, our model considers various factors that influence the likelihood and impact of vessel activities, such as shipping flux density, distance between ports, trade flow, and centrality measures of transportation hubs. Accordingly, this paper introduces transformers to gravity models to rebuild the short- and long-term dependencies that make the risk analysis feasible. Thus, we introduce a physics-inspired framework that achieves an 89% binary accuracy for existing and non-existing trajectories and an 84.8% accuracy for the number of vessels flowing between key port areas, representing more than 10% improvement over the traditional deep-gravity model. Along these lines, this research contributes to a better understanding of NIS risk assessment. It allows policymakers, conservationists, and stakeholders to prioritize management actions by identifying high-risk invasion pathways. Besides, our model is versatile and can include new data sources, making it suitable for assessing international vessel traffic flow in a changing global landscape.

Figures (7)

• Figure 1: Non-indigenous species carried by ballast water during container shipping.
• Figure 2: Global Shipping Network 2017--2019. Edge color and thickness are relative to the number of shipping activities per route, with darker blue and bolder lines indicating routes with higher activity levels. Port sizes in color-coded circles are scaled according to shipping fluxes to highlight their port capacity.
• Figure 3: The experimental pipeline for predicting ship traffic flows with gravity-informed models, including the assessment of environmental similarity used on the ballast water risk assessment case study. The process begins with identifying and verifying predicted links between source ports and target regions. Subsequently, key features are collected, and graph metrics are extracted so they can be used to inform the gravity-based model used to forecast ship traffic flow sizes. Concurrently, environmental data pertinent to the study regions is gathered and evaluated with the aim of computing environmental similarity metrics.
• Figure 4: Validation and test accuracy of classifiers in the trajectory link prediction task: (a) The performance of the classification task includes Haversine distance, sea route distance, and edge importance as features; and, (b) The classification task is carried out without the edge importance features.
• Figure 5: Framework of the Transformer Gravity model. The process starts with input sequences that are embedded and passed through self-attention blocks with multi-head attention, dropout, and layer normalization. This is followed by feed-forward blocks containing linear layers and dropout, resulting in the output sequence. The cross-entropy loss with log-softmax is used for training, while the Common Part of Commuters (CPC) is used for evaluation by incorporating commuting patterns $O_i$ from the input data.