Risk-Aware Digital Twin-Based Speed Optimization for CO₂ Emission Reduction in Short-Sea Shipping: The Istanbul–Piraeus Route

The maritime industry is under increasing pressure to reduce greenhouse gas emissions while maintaining economic viability, schedule reliability, and operational safety. This study proposes a risk-aware Maritime Digital Twin (DT) framework for voyage-level speed optimization and carbon dioxide (CO₂) emission reduction in short-sea shipping. Automatic Identification System (AIS)-based voyage records are defined as time-stamped vessel movement data, including position, speed over ground, voyage duration, and route-aligned operational information. These records are combined with meteorological forcing, bunker-price indicators, and port-congestion uncertainty to update a virtual representation of the Istanbul–Piraeus short-sea corridor. The mathematical core of the framework is a coupled partial differential equation–ordinary differential equation (PDE–ODE) model. The ODE component represents the finite-dimensional navigational state of the vessel, while the PDE component represents a reduced route-aligned hydrodynamic resistance field defined on a Hilbert space. This reduced PDE–ODE structure is not intended to replace high-fidelity computational fluid dynamics; rather, it provides a physically interpretable model for voyage-level decision support. The risk-aware decision layer combines Conditional Value-at-Risk (CVaR) and Distributionally Robust Optimization (DRO) to account for high-cost tail events and distributional ambiguity. The framework is evaluated through an Istanbul–Piraeus case study using processed AIS-based voyage observations and environmental data. The results indicate that reducing the schedule-driven baseline speed from 20 kn to approximately 16 kn can reduce CO₂ emissions by about 24% and CVaR-based operational tail risk by about 26% under the adopted assumptions. Sensitivity, ablation, benchmark, and Monte Carlo convergence analyses are included to clarify robustness and limitations.