\subsection{Baseline Physical Model} We compute the **theoretical speed over ground** $V_{\text{HM}}$ by solving for the equilibrium of propulsive thrust $T$ and total resistance $R_{\text{HM}}$: \begin{equation} R_{\text{HM}}(V) = R_f(V) + R_r(V) + R_a(V) + R_w(V) \,, \end{equation} where $R_f$, $R_r$, $R_a$, and $R_w$ denote frictional, residual, air, and wave resistance respectively (see Holtrop–Mennen \cite{Holtrop1972} for detailed expressions). The thrust is estimated from the ship’s installed power $P$ and propeller efficiency $\eta_p$: \begin{equation} T(V) = \frac{\eta_p P}{V}. \end{equation} The root of $T(V)-R_{\text{HM}}(V)=0$ yields $V_{\text{HM}}$.
\subsection{Limitations} \begin{itemize} \item \textbf{Data sparsity in polar regions}: AIS coverage is lower, leading to higher uncertainties. \item \textbf{Propeller efficiency assumption}: We treat $\eta_p$ as a constant; future work will embed a learnable efficiency model. \item \textbf{Real‑time constraints}: While inference is sub‑millisecond, integrating high‑resolution forecasts (e.g., ECMWF) adds latency; edge‑computing strategies are under investigation. \end{itemize} marvelocity pdf
\subsection{Training Procedure} \begin{itemize} \item \textbf{Train/validation split}: 70 \% ships for training, 15 \% for validation, 15 \% for test (no ship appears in more than one split). \item \textbf{Hyper‑parameter optimisation}: Bayesian optimisation (Optuna \cite{Akiba2019}) over tree depth, learning rate, and number of estimators. \item \textbf{Loss function}: Mean Absolute Error (MAE) on $\Delta V$. \end{itemize} Model training is performed on a single NVIDIA RTX 4090 GPU (≈ 5 min). ship‑agnostic evaluation pipeline
The final **MarVelocity** prediction is: \begin{equation} V_{\text{MarV}} = V_{\text{HM}} + \hat{\Delta V}(\mathbf{x}). \end{equation} 15 \% for validation
Recent work has shown that **data‑driven** techniques can capture residual dynamics missed by physics‑based formulas \cite{Bai2021, Chen2022}. However, many studies either (i) treat speed prediction as a black‑box regression problem without incorporating physical insight, or (ii) lack rigorous validation on out‑of‑sample vessels. Our contribution is two‑fold: \begin{enumerate}[label=\alph*)] \item We define **MarVelocity**, a hybrid metric that augments a baseline hydrodynamic resistance model with a learned correction term. \item We provide a large‑scale, ship‑agnostic evaluation pipeline, demonstrating superior accuracy and tangible fuel savings. \end{enumerate}