\subsection{Learning the Residual} Define the residual speed: \begin{equation} \Delta V = V_{\text{SOG}} - V_{\text{HM}}, \end{equation} where $V_{\text{SOG}}$ is the measured speed over ground from AIS. We train a Gradient‑Boosted Regression Tree (XGBoost \cite{Chen2016}) to predict $\Delta V$ from the feature vector $\mathbf{x}$: \[ \mathbf{x} = \bigl[\,\underbrace{L, B, D, C_B}_{\text{design}};\, \underbrace{V_{\text{HM}}}_{\text{baseline}};\, \underbrace{U_{10}, \theta_{\text{wind}}}_{\text{wind}};\, \underbrace{H_s, \theta_{\text{wave}}}_{\text{wave}};\, \underbrace{U_c, \theta_{\text{current}}}_{\text{current}}\,\bigr]. \]
\subsection{Hybrid Strategies} Hybrid schemes—e.g., residual learning on top of HM \cite{Zhang2023}—have shown promise but often require vessel‑specific fine‑tuning. MarVelocity differentiates itself by learning a **universal correction** that transfers across ship types. marvelocity pdf
\section{Discussion} \label{sec:discussion} \subsection{Interpretability} Feature importance (gain) indicates that $V_{\text{HM}}$ accounts for 38 \% of the model’s predictive power, confirming that the physics‑based backbone remains dominant. The top three environmental variables are wind speed, wave height, and current speed, aligning with maritime operational experience. nonlinear interaction among wind
\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). and ship trim.
\section{Conclusion} \label{sec:conclusion} We presented **MarVelocity**, a hybrid metric that blends classical hydrodynamic resistance modelling with a universal machine‑
\newpage \section{Introduction} \label{sec:intro} The global shipping industry transports over \SI{80}{\percent} of world trade by volume \cite{UNCTAD2022}. Despite advances in hull design and propulsion, a substantial fraction of fuel burn is attributable to sub‑optimal speed choices driven by inaccurate speed forecasts \cite{Mitsui2019}. Conventional approaches—e.g., the Holtrop–Mennen method \cite{Holtrop1972} or the ITTC‑1998 friction line \cite{ITTC1998}—rely on static ship parameters and simplified sea‑state corrections. Such models neglect the complex, nonlinear interaction among wind, waves, currents, and ship trim.
\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}
