\subsection{Ablation Study} Figure~\ref{fig:ablation} shows the impact of removing each environmental group from the feature set. Wind contributes the most to error reduction (ΔMAE = 0.04 knot), followed by waves (0.03 knot) and currents (0.02 knot).
\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
\section{Conclusion} \label{sec:conclusion} We presented **MarVelocity**, a hybrid metric that blends classical hydrodynamic resistance modelling with a universal machine‑ The thrust is estimated from the ship’s installed
\begin{table}[H] \centering \caption{Speed prediction errors (knot) across three methods} \label{tab:accuracy} \begin{tabular}{lccc} \toprule Method & MAE & RMSE & $R^{2}$ \\ \midrule Holtrop–Mennen (baseline) & 0.28 & 0.42 & 0.81 \\ XGBoost residual (ship‑specific) & 0.14 & 0.20 & 0.94 \\ \textbf{MarVelocity (universal)} & \textbf{0.12} & \textbf{0.18} & \textbf{0.96} \\ \bottomrule \end{tabular} \end{table} integrating high‑resolution forecasts (e.g.
\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 $V_{\text{HM}}$.